[DakotaGator]

...and he was an instructor at the Air Force Fighter Weapons School. The flyers call that institution “Top Gun.”

"Top Gun" was a Navy program. "Red Flag" was an Air Force program. Both have evolved and changed names. Don't believe they ever shared names.

[USNBandit]

They didn’t share names and Top Gun was always officially the Navy Fighter Weapons School, and will always be known as Top Gun. An exceptionally expensive opportunity, but a real blast.