Interesting question!
The Army doesn't use fighter aircraft, very few fixed wing, and mostly helos.
The Air Force does deploy PJ's and Combat Controllers who are definitely on the ground in harms way.
The Navy has SEALS, which in itself is extremely hard to get assigned to. I don't know how many SEAL officers would be allowed transfer to Pensacola and become a Naval Aviator. I do know of a Marine Pilot who later became a Naval Flight Surgeon.
You might want to consider the Marine Corps as their philosophy is "every Marine is a rifleman." Also all Marines must go through TBS which involves infantry tactics. Also the Marines do have a need for fixed wing fighter pilots. Someone else will have to chime in on the chances of starting out as a Marine Infantry officer and then transferring to flight training. I'm sure it has been done, but I don't know what the chances are.
But remember, the needs of the Corps (or whatever branch you serve in) will come first.