Great question. As a pilot and physician, I've looked into this. There isn't much for a civilian in terms of a fellowship. You can become an FAA medical examiner and give physicals to pilots. This requires surprisingly little in terms of actual training (about a week in Oklahoma City). Anybody can do it. They obviously prefer internists and surgeons, but they'll accept anybody (I know of a dermatologist). My flight physician is a general surgeon who provided me with some great information on this. You basically submit your name to the FAA and they contact you when a position opens in your area (there's a limited number per capita). Then you go to Oklahoma City for a week of training, which is primarily in how to fill out the paperwork correctly, and bam! you're an examiner. I suppose they figure any physician can do a basic physical, so they let about anybody do it. If you want to do hardcore aerospace medicine, the military is probably the way to go.