I have not been able to find an elegant phrase to use, but my guess is that something like "jefe de los médicos de aviación" o "médico principal de aviación" should convey the meaning. Perhaps I am misunderstanding, but I would have thought that "cirujano de abordo" implied the doctor accompanied the crew on its mission. In contrast, a flight surgeon is not necessarily a part of the plane's crew and I suspect that, although most flight surgeons do spend time in aircraft, in most cases they do not spend that much time as part of an air crew. The role of a flight surgeon includes care of the air crew with respect to aviation issues but also monitoring their fitness for duty and general medical care, tasks much better performed at the airfield than in the air. In the case of a Naval flight surgeon on deployment I suppose one might refer to a "médico de aviación de abordo" on an aircraft carrier but I hope there is a better term to describe that role.
As an aside, I do not know whether Spanish follows the English pattern of calling these doctors "surgeons" but my dictionary suggested "médico de aviación" rather than "cirujano de aviación". The English term "flight surgeon" is correct but the doctors in question are not necessarily surgeons. The title is traditional but not really an accurate descriptor; it is one of the illogical parts of the language.