What is the breakout by service branch for FAA ATC specialists with military backgrounds?
All military services in the US have Air Traffic Control MOS codes and training, except the Coast Guard. Army, Navy, Air Force and Marines all have it.

I don't know of any source of data that tells me if an ATC controller is a veteran, and of what branch of service. As far as I know, the FAA does not discriminate on the basis of which branch you were in when you were awarded the ATC MOS upon completion of training.