To get a high kick, you just have to reach for higher and higher each time. It's good to practice on a mark, have a goal you can kick at. Push it more each time. At Warriors Realm we do them as fast as we can repeatedly, which is very good because it loosens your tight muscles too. Practice often too, in order to keep the flexibility you have gained each time.
I also do this activity for every kind of kick, which is:
fast kick, hold, flex, hold, keep the balance and stay in that position trying to extend your flexibility more.
I also do this activity:
Raise one leg sideways, straight body, as far UP as possible.
Same with raising legs backwards, frontwards while standing in the same manner. Not bending any other part of body.
I think it also does pay to be flexible when doing kicks in the long run, thus stretching, not just splits, but get your knees and legs behind your head too, gives you more room to extend those legs anywhere in mid air. I mean, if you are kicking but your inability to be flexible is stopping you, then, stretch it out. I know lots of martial artists who take up gymnastics and extreme flexibility activities.
I found doing the splits frontwards, meaning one leg in front, one leg in back makes it easier to then do it sideways.
Also, your ability to flex out your muscles increases after cardio activity, and in warmth, which is good to know if you are building up your flexibility.
I think the main thing that has helped me excel in kicks is the touching your toes straight legged stretch. I can now pretty much put my head between my legs, can reach way past my feet, it looks weird, but being that versatile is good for lots of kicks.