EM residents often staff aeromedical rotor flights. In the real world, aeromedical is nearly always done by RN-RN, RN-paramedic combinations. It costs too much money to staff flights with MDs, too low yield. I am sure sometimes a very special situation or rich person will lend itself to a physician-staffed flight.
So, if you are doing your EM residency, you can fly. If you want to work as a flight medical person, you can do that without going to med school.
Paramedics and nurses do it nearly everywhere. THe only caveat is unless you are in an area that has no paramedics or nurses, you will have to pay your dues on the ground first.
Where I used to work as a paramedic (ID), you needed like 5 years of ground service to apply.
In AZ, they hire people fresh out of school and pay well.
Hope this helps