I'd have to agree that this doesn't sound like WT/WC kicking, but that's not what you asked, you wanted advice for flexibility, so here'e my two cents worth.
Most people train for flexibility by doing static stretching, ie. trying to touch their chest to their leg while sitting on the floor, or any type of variation of that. The problem with that type of stretching is it doen't mimic the movement that you are stretching for, namely kicking.
To remedy this you should practice dynamic stretching.
first exercise: swing straight leg to the front as high as you can. Hold your outstretched arms out in front for a target.
second exercise : swing your leg out to the side stretching the inner thigh, again having your outstretched arm held out for a target.
third exercise : looking over your right shoulder swing your right leg to the rear as high as you can, torso will be inclined forward on this stretch. (And then repeat for left side)
IMPORTANT: warm up before doing these stretches. Many people think of streching as warming up, it's not. Run in place, do a stationary bike, jump rope, whatever to get a light sweat going and heart pumping a little, then perform these stretches. I do 3 sets of 10 of each stretch. Also don't try to go too far too fast. You may throw something out you'll want later. So progress slowly.
Then after your workout do the old fashioned static stretching as your cooldown.
Another tip. When kicking, practice slowly to bring more muscle memory into the kick instead of just relying on momentum.
Hope this helps.
