What catch-phrase used by veterans instantly identifies in which branch of service they serve(d)?

That's too easy!!
"King of the Battle".........Army
"Whut??".......................Marines
"swhoosh".....................Air Force
"Mommie!!!!!"................Navy

Hooah

Airdale, Amp-Tramp, Stitch Bitch, Load toad, red shirt, hanger queen

USN, USCG and USMC: Sir, where is the Head?
Army: Sir, where is the Latrine?
USAF: Yo, buddy... where is the men's lounge?
(And as you can see, THREE out of five know the correct question and response)

Pop smoke, Get the hell out of Dodge, Say again, Coffee black 1 each,

The Air Force does need something. We used to be called bus drivers and was always asked what time the bus left/

Didn't See: in the rear, with the gear

The last response from us Air Force guys is wrong. It's a cappuccino, not a macchiato! We sometimes have to watch our figures, because nobody else will!

I would have to say SNAFU

Heard Understood Acknowledged = HUA= Hoohah. HUA originated with air force.