I've done dance, gymnastics and karate, with kicks probably being my strength in them all, so hopefully i'll help a little bit it'll probably be explained awfully but hopefully you'll get my points..
You don't need to be flexible to have good kicks, I could kick my leg to my head way before I could do the splits, you just need to make sure you have good form- try to keep you core tight when you kick, don't aim for height when you're first training them, just try to keep both legs straight, and your heel on the floor. you could also try an exercise i do now that tones your thighs and helps with kicks- step back into a deep lunge (keeping your core tight) and pull you back leg through so you end up standing doing a kick. do 12-15 of these on each leg, and try to do 2-3 sets; my left leg is no where near as flexible as my right so i'm doing these exercises to increase the flexibility in my left leg.
Some people can't do splits because of genetics. I taught myself to do scissor splits and oversplits (when you do splits past 180 degrees) when I was about 14 in about 2 weeks, but could never manage to do a proper box split just because my hips simply wont allow me to do it, i'm sure i read on a dance forum that only some people can do box splits because of the way their hips are designed.
The best thing to do is just stretch as often as possible, at one point i was stretching twice a day (which was too much as now i have a bad hip from it), aim to stretch every other day, and even if you don't get your splits any stretching will be beneficial to martial arts