I know it's a dead thread but I think I can shed some light. And give some advice.
I joined the Canadian army fine with flat feet, they did cuase shin splints from time to time. Usually when I was overtraining anyway. I had collasped arches but my feet are flexible which is why I was still allowed in. But I did have to get a note from my doctor saying it was ok. My doctor also said that I should take ballet to help with my feet and that in some cases you can rebuild your arches (there is evidence of this). I never did ballet and I tried some exercises with limited success. I passed all my training just fine with few difficulties related to my feet. I went onto to do mountain man, army run, crossfit teams and hockey. I got shin splints pretty bad sometimes and just rested. But then I got runners knee that is horrible. So I have for sometime now been working on my feet. As follows:
Get minimalist shoes, (vibram 5 fingers, vivo barefoot) I use moc3 with a 2mm rubber bottom. Nike free's and merrels minimalist trail runners are good for transition but have limitations as there is some padding still.
I started with 10 min runs but now I can do 10km. Mind you I was running much farther in normal shoes to start. You will naturally switch to a forefoot strike.
I also took the padding out of my hiking boots for rucksack marches and make an effort to keep my arches lifted while rucking.
I also lift my arches and bend my knees slightly for timed intervals, again start very easy on this. Eventually leading to balancing on one foot and not letting your ankle roll inwards (pronate).
You can do calf raises, for me this is too much with all the above. Try to point your heels outwards at the top of the raise.
And finally use a golf ball to massage the bottom of your foot to brake up old scar tissue.
My progress so far has been great with my right foot. I can actually see my arch. My left foot used to be crooked when standing on it and completely pancaked to the ground. It is now straight and slightly less pancaked. There is plenty information on the web, with people who have had amazing success. I would recomend talking to a doctor first to see if it would help your feet.