Flexibility in the groin is very important. I recommend strongly working on stretching your groin and hamstrings regularly if you're making drilling high kicks a priority.
I have been training for a couple of months now and I still not have improved in high kicks. What muscles do I need to be stretching to be able to throw that high kick with good form and without straining myself?
But improvement in high kicks, for people who can actually kick high, usually isn't an issue of flexibility. If you can get your leg up there, then usually it's an issue of form, getting the hips and lower back engaged, using weight properly, following through properly, etc. I strongly recommend working with an instructor.
I always think of throwing kicks a lot like golf. There are some things that you can learn watching tape, doing specific drills to improve parts of your technique, etc. but there really is no replacement for having someone with a lot of knowledge critique your particular form and fix your mistakes, because they are often so particular and such an issue of feel.