Flat feet are something that I see quite regularly and I find it quite sad that the advice people have been given has fallen short of actually helping them. When I get the Glutes (Bum) working for people, flat feet have a tendency to regain their arches, foot pain tends to dissipate and activities like hiking and running become something that people can consider without pain again.
Foot and ankle problems are common but often the common denominator is the Glutes. If your Glutes are weak and stretched - chances are that they are because most people work in offices where they sit for long periods of the day - they become overpowered by the inner thigh muscles (Adductors). These pull the knee inwards - creating the knock knee effect.
When the knees are pulled inwards this creates a rotational force on the knee. As a consequence the feet flatten and/or turn outwards which creates more stress on the knees and ankles.
Running, invariably is out of the question because even walking probably hurts.
Generally the advice is to strengthen the ankle with balancing exercises or banded exercises in an attempt to make the ankle and foot muscles stronger and often orthotic inserts are recommended to correct foot position to relieve pressure on the ankle and knees.
However, the problem often remains because the therapist often hasn't looked high enough up the chain to the hips (or even beyond) As an AMN Practitioner (no you haven't heard of it, that's fine, I'm a rare breed) I have the ability to check the whole body - often I would consider the Glutes first as a likely candidate in the flat foot problem but it isn't always the case however it often is involved.
Get your whole body checked to solve your flat foot problem in hours (of treatment) not months or years of exercises, resistance bands and pain.