Flying clubs were a real thing in the 1920's, with golf sometimes being incorporated as a feature.
Here are a number of examples -
Wauhilla Aviation & GC, Olema, CA
Yolo Fliers Club in Woodland, CA
Lansing Airport GC, Lansing, IL
Bradley Hills CC in Bethesda, MD was once known as Washington Aviation CC
Aviation CC (aka Lochhaven) in Pontiac, MI
Twin City Golf & Aviation Club (aka Michicago CC) in Benton Harbor, MI
Aviation GC in Bendix, NJ
There were plans for a public course to be known as Airport GC in Akron, OH. Not sure if it was ever built.
The Woodward Airport in Woodward, OK was turned into Twin Lakes GC in the early 1930's.
When Clewiston GC in Florida was being built by Stiles & Van Kleek, the land for the proposed second 9 holes was used as an airport.
Langford's West Palm Beach GC was taken over for the expansion of the airport there in 1942.
There were a number of courses built on Air Force or Naval Air properties for use of the officers including reports of Donald Ross building a pitch and putt course at Maxton Air Base, but that is a different story. The connection between the military and golf is probably deserving of its own thread.
Sven