Flying runs in the Sarnac family. If Carl didn't serve in WWII, we're still ready to claim that his uncle on his mother's side of the family did - and he was a pilot as well.
Lt. Brannigan signed up to serve as a pilot during the war - but only if he could fly an old-fashioned barn-stormer. He worked with Lt. Hanley on a recon mission in the episode "The Flying Machine" during which they both nearly got killed.
And it was his love of flying which he passed on to his nephew who in turn instilled it in his son Raynor and then tried to do the same for his grand-daughter.
As a Theory of Relateeveety, this is all supposition....
I'm also willing to entertain the theory that Brannigan and Carl Sarnac are the same man, with a 20 plus year age difference. Perhaps he had to change his name to avoid prosecution for something he did during the war.
But having never seen 'Call To Glory', I can't propose that theory in case something came up in the show to contradict it.....