Flat feet are not the problem people like to think they are.
When I was in high school, I was a gymnast. I became an all-American gymnast. And I'll never forget going to one of the first sports medicine physicians in the world, who looked at my really flat feet and said, “You can't be a tumbler.” And I said, “That's really strange to hear because I'm already one of the best in the world.”
There's no strong evidence to back up the idea that flat feet need support. The real issue isn't about whether your feet are flat or whether you have high arches. It's about whether your arches are strong, whether you're using them so they become strong and resilient and flexible.
People with high arches sometimes need to work on flexibility. Flatfooted people often just need to work on strengthening. And the best way to strengthen your feet is to be barefoot or in something like Xero Shoes, which are incredibly, incredibly flexible and give you all the fun and benefits of barefoot, but with a layer of protection and comfort. The gist is that you need to be moving your feet, to use your feet, which can strengthen your arch.
The other issue is sometimes people will tell you you have a problem simply because you have flat feet, when they don’t really understand the biomechanics of it. Maybe you've got a problem not because your feet are flat but because you're wearing some big, thick, stiff hiking boot or hiking sandal that doesn’t let your foot move, and so your ankle, your knee and your hip are trying to do the function that your foot would do if you let it move naturally.
Anyway, all that said, once again, try the natural approach. Don’t worry about whether you have flat feet. Just develop some strength and resilience, and let me know what happens.
Take a look at this article, too, about flat feet and high arches.