The Flying Ace is a man in his physical prime, often right at the confluence of youthful exuberance and age-worn experience. Variations on this character often rely on altering the character's age to adjust that balance of influences. For you younger folks, Poe Dameron of The Force Awakens is so typical of the archetype as to be iconic in its expression.
Like his ground-bound counterparts (racers and riders), he's got a competitive streak and a certain penchant for mischief- even as an older, more sober-minded man. This is often the basis for his considerable charisma, as his repeated practice of his core habits and skills instills a mindset of competency in adversity born of seeking and overcoming challenges that test him. He is, very much, an Alpha Male sort of character- and often finds himself in positions of leadership, becoming more formal and important as he ages. (e.g. Roy Fokker of Macross fame)
His adventures feature the display of his skills as a pilot, both in the coming and going to the sites of his adventures, but often in the formulation of the conflicts as well as their development and resolution. While he is capable on his feet (and often is quite capable of two-fisted action, good with his sidearms, or both), he's routinely deficient in highly-specialized skills or fields of knowledge that fall outside his core competencies- he's a Man of Action first and foremost, like James Bond. (e.g.
He routinely encounters his opposite number in his adventures, either a literal recurring nemesis or simply an enemy ace pilot. If this antagonist is not the chief antagonist, then he will be one of the major lieutenants to that mastermind and his decisive defeat is often the signal that the climax of the adventure just hit. (Otherwise, it's that of the mastermind directly.)
His adventures often involve McGuffin hunts, which drive the plot; this is not a mystery subtype, as the Flying Ace is not a detective. This is often a way to integrate the Ace into an ensemble cast where he operates as an equal on a team instead of a master or subordinate in a (para)military unit. Attacking enemy bases, or defending their own, is a regular part of his adventures; the former as part of the final act, and the former as the initial act if not the inciting incident.
Because he's an ace, even if he's using a known real aircraft his specific plane is an "ace custom" model tailored to his specific qualities in order to maximize performance- a real-life trope turned genre fiction trope that carried over to newer forms, such as Mobile Suit Gundam and the many Ace Custom models used by Char Aznable. His counterparts will often also have their own customs; these will routinely be visually as well as technically striking and impressive.
Check out his blog, Walker's Study, for more good articles on science fiction.