Does movement speed affect DPS of movement skills?

... like leap slam or cyclone (bonuses on gear to movement speed)?

No, unless the execution speed of the skill is affected by movement speed and that's the case only for lightning warp.

What about this line (cyclone description from the wiki):

"

High attack speed and low movement speed allows you to hit a single enemy several times, with higher movement speed it's possible to start another Cyclone sooner.

Wouldn't 'start another Cyclone sooner' mean more damage?

Think of cyclone as an AoE that pulsates at 160% of your attack speed and moves at 70% of your move speed. Moving faster doesn't change its pulse frequency, they are entirely separate, with low move speed you save mana and with high move speed you get more control.

But movement speed affects cyclones dps, no tool tip, but definitely kill speed. Just test it on atr and/or with movement flask. U do same dmg in shorter time, meaning more dps. If u use flask on boss, i kill it faster.

It's possible you're doing the cyclone stutter trick with really high move speed. They did something about that but it seems it's still possible, just a bit harder to pull off.

So why do people insist on getting movement bonuses for cyclone? You just apply the damage more efficiently over distance if you move quicker with cyclone?

Since Cyclone was changed to deal damage immediately when used high movement speed definitely increases its dps/clear speed even against stationary single targets.

agree with Raics.
the real-time DPS of Cyclone isn't affected by Movement Speed bonuses in terms of game mechanics, but it is affected by what the player can do with the extra control Moment Speed grants.
you can click and hit the same target again faster, so you have more DPS against it.