My daughter and I have extremely flat feet. I snowboard and she ice skates without any problem.
I have orthotics, but they hurt my feet bad. They are made of hard plastic and fit in your shoe (sort of) and push your foot up where it was comfortable being flat. Shoes themselves are not comfortable, those inserts don't make it any better!
My thoughts are as he does more exercise, he will develop muscle and strength. Is there more to it for him? Is he getting shin splits? Sometimes that is associated with the wrong shoe for the sport and or improper running technique. So if I buy a cheap ice skate for my daughter and she jumps, she will very likely injure her ankle. If I buy skates that are too stiff (too advanced), she may get fractures.
I think you have to provide more information about the weak ankles and the sports he is interested in.