Hi kakaislegend and Helzbells
A recent publication of the AAP on flatfeet and kids Vol. 123 No. 3 March 2009, pp. e386-e392
Flat-Footedness Is Not a Disadvantage for Athletic Performance in Children Aged 11 to 15 Years -- Tudor et al. 123 (3): e386 -- Pediatrics is all I could find on the subject.....
The people I have treated with flatfeet and pain problems have found the best solution to be a good inlay. This should be tailormade and fit all your sports shoes.
Shinsplints is a different thing alltogether....you have to be careful then. Once you are allowed to restart sports, the barefootedness during martial arts training should not be a problem for the flatfeet at all. You are being very active at that moment and will only strain yourself if you are held in some (strange)position for a longer period of time.
good uck to you all
Esther