He was for eight months, but was medically mustered out, an insurmountable (in their opinion) problem with rigid flat feet. His feet don't relax even at rest and he was really messed up limping around by the time he was two days away from completing his School of Infantry course. But, he earned his Seagull and Beachball emblem first. 
Bless his heart. After all that time, I would think they would have kept him and had him doing something else, other than Infantry. Maybe he could go into the Navy?
My mother was a Navy nurse, and my dad was a corpsman during WWII.
I'm not sure if being in the service is what made them feel the way they did...but I was born with very flat feet, and both of them were determined that I would not be flat-footed. I wore the ugliest corrective saddle shoes until junior high and only got to wear "pretty" shoes to church, and then immediately change into the "uglies". I even had to wear "old lady" Grasshopper sneakers and was never allowed to go barefoot.

I have the highest damn arches, only the very outside of my foot will leave a footprint. I have trouble buying shoes and boots, because my arch won't fit into the shoe.

M has flat feet like your son does. His mom had him in corrective shoes til he was in 3rd or 4th grade. She gave up after he "lost" 2 pair. His feet won't bend, flex, nothing. He doesn't have trouble finding shoes.