Adding movement adds a level of difficulty because you now have to make sure to keep the distancing consistent while still being able to rapid fire your strikes with a high level of control.
Adding the kick is yet another level of complication added to the drill. You can see that the partner who is not striking is equally challenged in having to make sure the timing of the movement is spot on.
As with most combinations, when you add footwork, you will start your strike combo with the lead hand. Make sure your 3 count combo is very comfortable before adding layers of skills like half mooning.