for the person with flat feet -
you need to correct your bio mechanical movement if you can, by retraining your body to walk and run correctly.
try and go barefoot as much as possible, as most shoes especially those with thick heels mess up your bio mechanical movement even further and is usually the cause of flat feet in the first place.
it's the shoes causing you to use incorrect movement, our bodies were not designed to be wearing shoes.
you should be using the balls of your feet, etc.
problem with barefoot is, it takes ages to get used to and you wont be able to run barefoot at all without injuring yourself unless you have done some serious regular mileage walking barefoot. i tried running barefoot and i injured my knee, got several blisters and was in agony for days.
tbh i couldnt be bothered doing all of that and i just bought specific running shoes for my type of feet (flat footed - collapsed arches). i'm still flat footed, but i can now run without pain.
tbh it's best to try and solve the problem at the cause rather than try and fix it after it's caused an issue.
wearing vibram's is one way to do it or any other minimalist shoe, but the earlier you start the better. women don't usually have an issue because they normally get a decent arch in their foot from wearing heels regularly.