In my experience, kicking flexibility improves with, well... more kicking. The more you kick and the more comfortable you are utilizing your hips in that way, the easier it will be to throw dynamic kicks. I couldn't kick head height two years ago. Now, especially after warming up, I find it to be relatively easy. It's hard to gauge that on the bag, too. I find that, when you put a real person in front of me for light sparring, I can gently put my shin against the side of their head without too much difficulty. Just make sure you warm up with some rope skipping, or a run, some shadowboxing, and some low/mid kicks before working on your high kicks.
And yes, your instructor's advice is good. Some people don't pivot as much. Me, I pivot to that degree. Here is me kicking:
4:21 is a good example of how far I pivot. Ignore the shitty boxing and shitty left kicks, by the way. :wink: But you can see that, at the moment my kick lands, my heel is usually pointed more or less at the target, or it's just slightly less than.