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.
I would say there is a difference between good technique and properly performing high kicks.
You can develop good technique practicing with lower kicks.
For example, a side kick involves specific movements, from chambering to the final leg extension.
These technical movement can be trained at the height your comfortable with. That could be at knee height.
You're probably referring to the "half turning kick" (sometimes called just the "turning kick", "twisting kick", or "45 degree kick") which goes by various Korean names, depending on your organization: "bit chagi", "paldung chagi", or a "bandal chagi".
You can see it here: