I deployed as an Army flight nurse on Blackhawk helicopters two years ago. Unfortunately, there is no way to be a permanent flight nurse in the Army. That job doesn't exist. I am an ICU nurse and had the opportunity to do this job overseas but when I came home I went back to the ICU.
All Army nurses start out as medical-surgical nurses and after about two years have the option to specialize. The ICU is a specialty option. The first step is do the time in med-surg then apply for the Army's 4-month critical care nursing course.
If you want to be a flight nurse, the better way to go is the Air Force. They have opportunities for aeromedical evacuation that involves non-critical patients and critical care air transport that requires an ICU nurse, respiratory therapist, and intensivist. They mostly operate on fixed wing aircraft- C-130 or C-17.
Of course, this all could change but that's how things are right now.
Unless you really want to be a nurse, I recommend becoming a paramedic. They have permanent positions in both the active Army and the National Guard. I deployed with a NG unit and they were awesome. A lot of them worked as ground or flight paramedics in their civilian jobs. The NG paramedics did more missions that the Active Duty medics too. The National Guard has a stateside mission (I.e. search and rescue) and their flight hour requirements are the same as Active Duty.