The AVG was not part of the U.S. Military, they were mercenaries. After the war began they were inducted into the Army Air Force, at much lower pay. Claire Chennault warned them that if they went home, their draft board would be waiting for them at the bottom gangplank when they left the ship to draft them into the infantry. Most stayed.
They were mercenaries on paper, thats why they were paid more than the military. But most of them were military pilots eleased from the American service to go do the job even as the military was building up for our inevitable entry into the war.
They were intended to help blunt the Chinese advances towards British holdings and help preserve British bases for allied forces while Americans built up and were not officially part of the war.
After they were disolved they went back to being military pilots and mechanics, with the medical personnel returning to the medical field stateside.
Greg Boyington broke his contract with the Tigers and went back to the Marine Corps early.