I am fully flat-footed. No arch, whatsoever. I was given custom orthotics by the CF for it.
To give you a numerical idea, the specialist I saw four years ago @ LFCATC Meaford used a 12-point scale to measure flat-footedness, with '1' having too-high of an arch and '12' being entirely flat footed, with no arch at all. Guess what I am?
Anyway, point is, I'm in the CF, have been in both the reserves and the reg force, and thus far it has not hindered my career in any way. As I said, the CF gave me orthotics for the issue with absolutely no hassle.
I do, however, have the occasional wildly painful Charley Horse in my feet from the muscle(s) in my flat feet seizing up when I'm walking around barefoot...
Best of luck