I would begin by reaching out to recruiters in your area. Do some serious research as branches vary. I am commissioning in the USAF reserves and there is only one recruiter who does medical in this area (Tampa Bay). You could start by reaching out to Ssgt Alex Asencio 813-523-8864
Nurses (BSN and higher) go to Officer school, not basic training. For the Air Force, this is an 8 week course at Maxwell AFB in Montgomery, AL. Once you complete Officer training, there is other training required. It is dependent on your job. Flight nurses attend flight school, SERE, medical, etc. Its approx 9 mo of training all together.
Be patient though, the process is VERY long. I have been at it for 2 years and just completed my flight physical and am waiting for the Surgeon General to sign my waiver (heart murmur) before I can swear in. Even after that, I have to wait a few more months before going to Officer training. The selection is competitive and they will want to know every detail of your life, health history, and career experience.