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A zoomie is a slang term for a member of the air force.
A Zoomie Chick... or a Marine Mattress if training at an all-services school.
Airman/men (Notice the title it is capitalized, this is for both Officer and Enlisted personnel).
That isn't a nickname, that's what they're called officially.
Many branches refer to Airmen as "Flyboys" or, in general, the "Chair Force"