I don’t think that you can enlist to in the Air Force to be exclusively a phlebotomist. But if can enlist as a medical lab tech (MOS 4T0X1 – MEDICAL LABORATORY) where phlebotomy is part of the job. That is if that MOS has openings.
I was a Med Tech in the U.S. Army for 18 years. And I’m still a Med Tech as a civilian.