I have a mild case of flat feet (like, I reckon, 1 on the picture below). I'm also often kind of awkward in my movements when performing high kicks and occasionally have balance issues (I don't fall to the ground altogether but sometimes fail to complete the movements smoothly). Come to think of it, not only high kicks. When I perform ushiro geri, I notice that my supporting foot often tilts onto the outer edge making my stance less stable (I'm not sure whether it has anything to do with my flat feet or is a separate condition). Since I've had years of practice (including the fact that I've been practicing at home on my own for just about the last four years), I've started to think that it's not my fault, and the two problems, flat feet and the described flaws in my technique, are connected. Are they? I shouldn't blame myself, should I? I'll never achieve really good results without treatment, shall I?
This has nothing to do with flat feet. If it would, you would tilt your ankle inwards since flat feet are about a lack of supportive structures on the inner side of your feet. What you experience is a tilt outwards, which does tell me that you actually lack weight on your foot and, thus, it is about your technique and not your medical condition.
Therefore, if you have problems with ushiro geri like the ones you describe, this is either due to bad technique because you do not set the foot correctly and move weight on it to have proper grounding and hip rotation, resulting in balance issues, or it is due to bad technique coming from focusing on height instead of technique but not supported by the flexibility needed. Probably a bit of both factors. Proper technique is much more important than height.
I have flat feet, I used to lack flexibility (especially in the hip), I had similar problems. What you need for a good ushiro geri is an instructor who improves your technique and constantly reminds you of your faults, and a stretching regimen. Having trained bad habits for four years on your own means you will need lots of training time to get rid of them. Training science assumes 2-4 times as many repetitions as you did incorrectly.
That being said: You can do something about flat feet and strengthen the arch of your foot and the ankle as well, even if it will not better your technique as such. It can support proper technique later, though. Balance boards (used on one leg) or simply standing on a soft surface on one leg for extended periods of time (until you can make ~60-90 seconds, 3-5 sets), at first statically and later with moving the other leg around slowly into all directions (keeping the upper body upright, shoulders horizontally, going down into the knee but not below 90 degrees if possible), helps to train the muscular structure that stabilises the foot and ankle, up to your hip. Bobbing on the ball of the foot (soft surface, heel not touching the surface, make sure you do not make evasion movements to the outer edge of the foot and distribute weight equally across the front of the foot) strengthens the muscular structures of your midfoot and stabilisation by the toes and ankle.