Did the old Flying A company get its logo from making aviation fuel?

According to information you can find at
http://www.oldgas.com
the Flying A logo came into existance in 1938 as Tydol Flying A gas. The Tidewater Oil company was founded in 1875. When J. Paul Getty gained control in 1937, it became Tydol. In 1956, the 'Tydol' was dropped in favor of 'Flying A'. The brand disappeared in 1966. In 1938, aviation gas was a miniscule part of the business of refining petroleum. The 'Flying A' logo was probably meant to connote smoothness and speed for your automobile.

There was also another 'Flying A' company formed by Gene Autry in the early 1950's to produce his TV and radio and other media ventures. It had nothing to do with oil.

The flying "A" had nothing to do with aviation fuel or, prior to 1937, the Tidewater Oil Co. The flying "A" was trademarked in 1932 by the Associated Oil Co. in California, which was owned by J. Paul Getty at that time. It only moved nationwide when Getty purchased controlling interest in the Mission Corporation formed by Standard Oil to manage Tidewater which it acquired in 1937. The "A" simply stands for Associated.
https://en.wikipedia.org/wiki/Associated_Oil_Company