How do we develop speed in the martial arts?
Correct body mechanics. Relaxation.
The first element of speed is having correct body alignment- ankles, knees, hips, spine, shoulders.
Everything moving in unison and in the same direction.
Training in the basics (kihon) of your martial art, along with attention to detail and regular diligent practice will help cultivate this.
Next layer in developing speed and flow in the martial arts is getting ride of muscular tension.
A dedicated stretching routine during the day and before/after practice helps with this.
As your practice, use that time to identify and isolate any points of tension. As an example, if you are practicing striking methods, after working out, are there any specific joints that are sore- elbow, shoulder, neck? Are you holding tension in these areas?
Add those specific areas to your stretching routines as you continue working through the martial arts basics. That is the “formula” for developing fluidity, flow, and speed in the martial arts.