Google "Flying Tigers" and you will find it was considered a "AVG" (American Volunteer Group), a private contracted "air force" that flew P40's and commanded by a man named Claire Chennault. They flew 1941 and 42. In July of 1942 the AVG was replaced and became under the command of the U.S. Military as the U.S.Army 23rd Fighter Group, then later the 23rd was absorbed into the 14th Air Force. The B-24 "Hot As Hell" aircraft was assigned to the 14th Air Force Unit.
Now whether anyone other than the orginal AVG fighter pilots and crews of the P40's can claim being a member of the "Flying Tigers" I am not so sure.