I have flat feet. It causes the muscles of the sole to tire easier from walking and standing and requires you to find flatter-bottomed shoes, but I don't see what it has to do with joints. There is no evidence that exercising is a bad idea when you have flat feet:
http://en.wikipedia.org/wiki/Flat_feet
(BTW, moving around as much as you can with bare feet strengthens the muscles of the sole and the "easily tired sole" problem goes away. I have taken to wearing ultra-thin soled shoes for this reason.)
If you are in bad shape, walking briskly is aerobic zone cardio. If walking isn't enough to put you in aerobic zone, you are in good enough shape to carry some extra load. It's about the most natural form of exercise available to man, instead of "athlete only". Old and disabled people go hiking all the time. Children carry backpacks on long walks to school every day. People carry their shopping home.