Welcome to Gaia! ::

Do you mean 360 kick/tornado kick/volley kick?

Tornado kick tutorial

Or do you mean spin/back hook kick?

Spin Hook Kick tutorial

Spin Hook kick in action

Did you even watch the videos I posted? The third video I posted is the exact same video (different uploader). Calling the kick Dwi Dolryo Chagi (spin round kick) is new to me but I suppose some schools call it that, I've always heard it referred to as Dwi Hooryu Chagi which is usually translated as Spin Hook kick or Spinning Whip Kick. Which makes more sense to me since it doesn't look like the roundhouse kick.

Usually the jump isn't noticeable at all. The video you (and I) posted is technically what most TKD consider a jumping spin whip kick. The jump isn't meant to get you vertical height, it's only meant to get just enough height off the ground to switching the feet simultaneously in the air (which is a faster way to turn than turning with your feet on the ground). Getting vertical height is incorrect (impratical for sparring), you'd have to bend your knees to liftoff to get the most vert and that'd slow you down and make you obvious to your opponent.

Unless you're throwing the kick for demonstrative purposes or whatever, which might explain why you'd actually want to get height. *shrugs* I don't do kicks for demos though so you're on your own with that.

Ignore them? *shrugs* The way you're doing it sounds like the way I'd throw it in competition (hopping to switch feet in air).

My guess is to get height you'll probably want to bend your knees deeper to get a better lift off and to bring your knees/legs in while you're jumping up. As your leg extends for the kick your other leg will want to stick outward in order to maintain your center of gravity and balance in the air or to stick the landing. Honestly even when I see the hook kick during tricking or board breaking, I rarely see the other leg chambered in the air while the kick is extended.

You could add a turning step prior to the jump (something called blocking or something like that, gymnasts do it, youtube it) though rarely done with this kick as far as I know, or you could bring your arms in and make your spin more compact to accelerate your body while spinning. In terms of actual vertical jump, you can increase the fast twitch muscle fibers in your lower body with pylometric exercises so that you have a more explosive lift off (a lot of volleyball and basketball players use pylometrics to increase their vert). Flexibility will also give you height in terms of your kicking leg reaching its target.

I wrote this in another thread.

As for the strength and speed of your kicks, you'll want to promote the fast twitch (type II) muscles for explosive power. You'll want to do plyometric exercises and most likely, you're probably already doing your share of these for basketball (the act of exploding up into a high jump for a rebound or a layup uses the same muscles and increasing your explosive power might increase your vertical). An example of a plyometric exercise is a squat jump, Muay Thai sometimes call them Thai Hops, basically you squat and jump, squat and jump, repeat. A quick google search brought up this website that has some nifty animations of more plyometric exercises to try.

Pylometric Exercises Animated