by flat footed, do you mean without shoes, or somehow eliminating the arch in the foot? if the latter, then it's not a good idea, if the former, then it depends.
You can do it, thought you can use shoes too, but make sure they are good for the purpose. Usually running shoes that are shock absorbing aren't that good because the soles are unstable, something you don't want with a lot of weight on your back in a squat or in your hands in a deadlift or lunge or whatever.
A lot of lifters squat with a weightlifting shoe that has an elevated heel, nothing wrong with that. The soles are hard, though, they won't give away as you push through the heels.
