Chucks/plimsoles or failing that bare feet for squatting.
Flat feet? get yourself a firm sponge ball (or a tennis ball), then stand on it under your heel - slowly roll the ball under your foot [you'll feel a scrunchy release as you do this] until it reaches your toes, at this point with your foot on the ball and your toes spread out - squeeze the ball under them. Another way is to start with it under your heel, roll it forward an inch, then roll from the outside of your foot to the instep - centre it again and roll it forward another inch, repeat from outside to in again; similar when you reach the toes.
This releases tension and adhesions in the foot musclature - allowing the muscles to work properly ie lift the arch.
Another exercise is to pick-up marbles with the toes, place them a foot away, let go then move them back.
Remember that if your fallen arch is being supported by shoe inserts/whatever - then the muscle will "fall asleep" as it's job is being done... which is akin to muscle wastage in bed ridden patients!
Take it "one step" at a time and good luck
TDM