My daughter has flat feet (more flat than yours) and she has improved her point. She can actually touch her toes to the floor. She did Pineapple's suggested exercise and toe rises regularly, along with some toe stretches. There are a ton of feet, arches and ankle exercises in the Internet if you google it. They really do will help you if you do them consistently. Here are some simple exercise you can probably do while watching TV too. Remember, the feet is a very integral part of a dancer. It is proven that exercise can and will help. So, if it is important to you to improve your point, you need to consistently work at it. Change will not happen overnight.
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As far as wearing high heels, I've heard some people think that. But I believe that is misguided. I don't know if it can strengthen arches but I do know it shortens the Achilles' tendon and can develop all sorts of other feet problems. In addition, very high heels makes the pelvic and spine tilt in ways that can eventually cause lower back pain. My thoughts are and it is pretty much common knowledge, high heels does not promote healthy feet, spine and back. So, personally, I would not recommend a purported "solution" that can perpetuate many other problems. And honestly, in my many years as a professional, instructor and student of dance, wearing high heels has never been recommended (by any individual whose opinion I respected anyway).