Movement Speed

Distance traveled divided by the amount of time taken.

I have taken the liberty of measuring the speeds of most movement skills. Excluded are ones that require monsters for obvious reasons.

Method:
All speeds are measured at the bottom of FM7, chosen as a simple flat plane where no angular launch can be considered, and friction is constant.

The time taken was measured from the first movement, and stopped at the last horizontal movement; what this usually means is the timer starts when the character first moves, whether that be the skill launching them forward, or them needing to jump straight up to begin. The timer is stopped when the character collides with the wall at the end.

All times are measured through FRAPS at 90 frames per second, taking usually two test runs and comparing with previous tests. There is an error margin of about 2%, from previous experience. There will be no videos posted unless highly demanded.

Units of Measurement:
As a standardized method of measurement, we will use the character speed displayed in the status screen. 100% signifies 100% speed, base speed. It is in fact true that 120% speed is 1.2x faster than 100% speed, and 140% speed is 1.4x faster than 100% speed, with a very small margin of error.

This table contains speeds adjusted for the new 150px/s speed after the Jump! patch. Any skills requiring (excessive) walking to influence it were removed from the table or striked. Testing is required to update these skills and conditions. The only movement skills missing now are Gigantic Backstep from Cannon Shooters I believe.
Results (Post-Jump/Legend):

Phantom Shroud:	950%	(1.20s)
Monkey Push + Momentum Cannon Jump:	~500%	(2.30s)
Magical Shift/Sudden Propel:	485%	(2.36s)
Monkey Push:	461%	(2.48s)
Swift Phantom (Haste):	416%	(2.75s)
Double Leap (Air Lift):	409%	(2.80s)
Elemental Shift:	381%	(3.00s)
Wind Walk:	381%	(3.00s)
Instant Acrobatic/Flash Jump:	352%	(3.25s)
Instant Soul Jump:	347%	(3.3s)
Ascend + Thunder (Boostered):	317%	(3.61s)
Demon Jump/Glide:	305%	(3.75s)
Wave + Shark Tooth (Boostered):	305%	(3.75s)
Maximum Acrobatic/Flash Jump:	295%	(~4.00s)
Exceed: Demon Strike:	272%	(4.20s)
Momentum Mechanic Dash:	270%	(4.24s)
Teleport:	N/A	N/A
Momentum Combat Step:	262%	(4.37s)
Wave + Shark Tooth:	244%	(4.68s)
Instant Jag Jump:	224%	(5.11s)
Instant Double Jump:	219%	(5.22s)
Soul Runner:	N/A	N/A
Maximum Jag Jump:	202%	(5.67s)
Recoil Shot + Float:	197%	(5.81s)
Walking Combat Step (115%):	195%	(5.85s)
160% Speed:	160%	(7.15s)
140% Speed:	140%	(8.17s)
120% Speed:	120%	(9.53s)
100% Speed:	100%	(11.44s)

Results (Pre-Jump):

Instant Acrobatic/Flash Jump:	422%	(3.25s)
Demon Jump/Glide:	365%	(3.75s)
Maximum Acrobatic/Flash Jump:	343%	(~4.00s)
Momentum Mechanic Dash:	323%	(4.24s)
Teleport:	~300%*	(4.45s)*
Momentum Combat Step:	292%	(4.69s)
3rd Job Instant Jag Jump:	268%	(5.11s)
Instant Double Jump:	262%	(5.22s)
Soul Runner:	245%	(5.6s)
2nd Job Maximum Jag Jump:	242%	(5.67s)
Recoil Shot + Float:	236%	(5.81s)
Walking Mechanic Dash:	189%	(7.24s)
Walking Combat Step (140%):	189%	(7.26s)
Walking Combat Step:	170%	(8.07s)
160% Speed:	160%	(8.56s)
140% Speed:	138%	(9.93s)
120% Speed:	120%	(11.37s)
100% Speed:	100%	(13.70s)

*Teleport is an adjusted value to account for the variability of walking distance, plus the nature of the constant distance it moves a character.
For some reason, 140% speed kept measuring to be 138% speed. I do not know why.

Jag Jump:

 Spoiler

1: 191% (7.18s)
5: 223% (6.16s)
10: 266% (5.14s)
~8% speed per level
Usage: For optimal speed, Jag Jump should be used the frame jumped off the ground, while holding the direction you want to move. This is a movement skill that does not carry momentum, most likely due to the Jaguar. The 20% speed increase from Jaguar Boost appears to be negligible to Jaguar Jump itself. More testing is required to see how Jump stat affects this.

Combat Step:

 Spoiler

Walking:
1: 123% (11.17s)
5: 132% (10.34s)
10: 146% (9.36s)
15: 170% (8.07s)

Momentum Step:
1: 137% (10.01s)
5: 190% (7.22s)
10: 235% (5.82s)
15: 292% (4.69s)

Holy pineapple Momentum Stepping with level 1 Combat Step is hard. This skill does not scale linearly. You get a large improvement with each point, especially if you use Momentum Step; bind Combat Step to a Macro key, and spam jump after using it. Do not hold a direction key, and do not wear Snowshoes. Holding an arrow key causes you to lose momentum when you hit the ground instead of sliding because you're trying to walk. If you do it correctly, the speed you gained from using Combat Step should transfer some into your jumping motion, causing you to jump further. By pressing your macro in midair, when you land it should automatically use Combat Step, which itself is sped up by the speed of your landing from a fast jump, etc. It tops off at a maximum speed that is higher than 292%, but not easily measurable since timing would have to begin after maximum speed is achieved (3 or 4 Combat Steps).
Additional Jump stat causes this to become slower.

After the Legend Update, Arans receive a buff to Combat Step that gives them passive speed, as well as a distance increase.
Walking Combat Step:
1: 165% (6.94s)
5: 195% (5.85s)

Momentum Combat Step:
1: 208% (5.5s)
5: 262% (4.37s)
There appears to be a significant factor of lag decreasing the effectiveness of Combat Step, particularly in terms of walking.

Mechanic Dash:

 Spoiler

For method, see Combat Step. It's the exact same thing except you get it at level 10, and it's better in every way including MP cost.

Flash Jump:

 Spoiler

Instant:
1: 259% (5.29s)
10: 324% (4.22s)
20: 417% (3.28s)

Maximum (120% Jump):
1: 213% (6.43s)
10: 270% (5.07s)
20: 348%s (3.93s)

Instant Flash Jump is when you use Flash Jump the frame you jump on. There's almost no difference between having Jump stat at all, except the number of Flash Jumps you use (more jump = less Flash Jumps, same time i.e. saving mana) Maximum Flash Jump is when you use Flash Jump at the height of your jump (in this case 120%). It's less efficient for traveling distances than Instant Flash Jump. It used to be the case that holding down the forward arrow key would reduce your speed due to losing momentum when contacting the ground. Either the way I do Instant Flash Jump is too fast to read this, or this case has been removed.

Teleport:

 Spoiler

Teleport scales linearly at all levels. Since it always travels the same distance, and always goes at the same speed (600ms), you can calculate its speed by "distance"/0.600)/125 ~= speed, plus a little bit more for the walking time the character will do in between teleports.

Recoil Shot + Wings:

 Spoiler

Fast (5): 234% (5.84s)
Fast (3): 236% (5.81s)
Lower levels are so pathetically slow, I don't have the hard drive space or the patience to record them, etc etc.
Just a simple macro with Wings and Recoil Shot, no bonuses. Likely could be faster with more Jump. Weapon Speed appears to be insignificant. My attempt at controlling momentum after using Wings resulted in significantly slower times (6.5s+).

Soul Runner:

 Spoiler

I didn't bother to "retest" this value, but I will be using the value I had found in previous testing some months ago. The results are 100/100 using a timer-based macro that used Jump+Soul Runner at the speed of its cool down, and walked (I'm 90% sure I walked)the duration of its cool down. I believe Soul Runner scales linearly, but achieves a significantly larger than linear boost by using Jump at the same time.
For optimal distance covered, after landing from Soul Runner, no direction should be pressed, and a jump should be used, and then walking continued since the jump will gain the momentum from Soul Runner to cover more distance than regular walking.

Double Jump:

 Spoiler

Level 1	183%	7.5s
Level 5	214%	6.39s
Level 10	262%	5.22s

Actual speeds are likely a bit faster (~5-10%ish maybe?) due to cross-server lag. All tests were done with Instant Double Jump, where it was activated as close to the frame leaving the ground as possible. Firstly, there's this inexplicable lag that occurs when I autofire my jump button. This doesn't occur on GMS, and is probably some sort of anti-botting measure in KMS, which means that while I can perform the jump rather quickly, I get ~15 frames per second, and ridiculous strain on my CPU so I can't actually record accurately, and the jumping doesn't stop for 10 seconds. I managed to overcome this with a different jumping method, which doesn't seem to have affected the results, but there seemed to be random instances where my Double Jump seemed to not gain its full forward momentum. The Double Jump animation did not appear, but I definitely jumped further than a normal jump; however, this is not the same as using a normal jump after repeated Double Jumps as that gets nowhere near the distance. I presume it's just some sort of bug with the skill itself but doesn't have a significant effect on its usage. Those instances I traveled at the same speed, but got more vertical distance at the same time which was weird. Holding down forward appears to have no impact on speed. I did not test maximum height jumps because of lag. I cannot reproduce it effectively enough, and it appears to be slower anyway.

Acrobatic Jump:

 Spoiler

Acrobatic Jump is performed in the exact same manner as Jag Jump and Double Jump; however, the base walking speed was increased from 125px/s to 150px/s, and thus the % scale has to be changed for this skill. This base speed applies to all characters, not just Mercedes. At level 1, Acrobatic Jump traverses FM7 in about 6 seconds, or 196% (228% for 125px/s walking speed), and 4 seconds at max, or 295% (343% for 125px/s walking speed). Instant Acrobatic Jump traverses at 3.25s or 362% (421% @ 125px/s). Acrobatic Jump was performed with 123% jump, as all Mercedes have at least 120% jump and I happened to have some jump bonus on which isn't a significant difference. Acrobatic Jump is too fast, especially since it's a 1st job skill and is the fastest skill in the game.

Demon Double Jump/Glide:

 Spoiler

Demon Double Jump performs at a very fast speed if done in an optimal fashion, i.e. instant like every other skill of this nature. It is not as fast as Flash Jump or Acrobatic Jump, but is the second fastest travel. Gliding is performed by pressing and holding down jump after jumping, and holding a direction. After landing, a fast jump and direction is required to maintain a good speed and flow, otherwise too much time is spent in midair transitioning from jumping to gliding, causing a significant slow down. It can match the Demon Slayer's Double Jump speed, but is often less fast and less efficient, though easier, and can be done across large gaps. The speed is faster than Demon Double Jump, but unachievable on areas that have long flat ground since they require you to land.

Magical Shift & Sudden Propel:

 Spoiler

Magical Shift uses the Jump key to activate in midair. After activating Magical Shift, you can hit the Jump key to launch further forward in the air, or change directions. The delay is set to 200ms (~210ms) in the data, but I could only get around 360ms~390ms when testing as the fastest on autofire. There appears to be some inconsistency at times, likely caused by lag where the second Magical Shift activates extremely quickly. This could also be an approximate 1 second spam delay between the second Magical Shifts which explains why it desyncs when I jump into a wall.

Sudden Propel appears to function identically, though Angelic Busters have a higher base jump, thus allowing them to utilize the second jump more easily than Xenon can.

The overall speed appears to be 2.36s or 485%.

Elemental Shift + Thunder Breaker

 Spoiler

Elemental Shift functions like any other Flash Jump, except when you push Up and Jump in mid-air, you do a high jump instead. Its speed is slightly slower than the more recent skills.

Thunder Breaker's Wave + Shark Tooth is listed for un-boostered and Boostered (I believe this is Fast (5) and (3), as I don't have SI). Ascend + Thunder is only listed for Boostered. They are both quite fast for travelling, especially considering they are attacks.

What I Didn't Test:

 Spoiler

Tornado Spin + Flying Assaulter
I do not have access to these skills without their long delays, so I cannot test their travel speeds.

Various speed and level combinations
Due to time constraints, not many speed or level combinations were able to be tested. If there is a specific combination you would like to see, ask in the thread and I will either explain it or test it.

If there is anything I missed or any questions let me know.