Could it be for someone who is ready to retire? I would imagine that a flag flown in a combat arena would be valued more by a warrior than one that flew over the Capitol...
A nice touch to be sure, but this isn’t news to any USAF veterans...
Many crews carry a flag or numerous flags when going on missions...they’re for themselves or for presentations to others like groundcrews who were directly involved in getting that particular aircraft ready to go.
As you alluded to, some are presented in retirement flag boxes, etc.
Or, given the way it was folded, could it have been in memory of some fellow pilot who was killed?