I know you didn't used to be able to with flat feet, but I think after lengthy research done by the Army they concluded the flatter your feet the less injury risk, so now you can enlist with flat feet.
[joke]During WWII, a young mountain man enlisting with flat feet was told the Army couldn't take him.
"Son, we can't take you with flat feet. You wouldn't be able to march a mile!".
"Ah shucks, that shur is too bad, I don walked 80 miles to git here, and I shur do hate to have to walk back!"[/joke]