Kicking high comes from the knee, point your knee where you want the kick to go and snap your leg out and back hard and fast.
Two simple things you can try when warming up your legs are:
very loose and fast, snap your leg back to hit your bum then thrust it out like a front kick except with toes pointing down, this develops speed.
Then raise you knee straight up aiming to touch the chest, again alternating very fast, this should help with the height. Do it over and over again as a warm up.
Then start kicking the bag or shadow sparring.
Otherwise concentrate on low kicks, smash the body and legs until he cannot walk and then finish with punches.