The historical truth behind the black pilot
Eugene Skinner, the black pilot, was based on the real-life Eugene Jacques Bullard (the filmmakers just changed the surname). He hoped to join the Lafayette Escadrille, but they stopped receiving applicants by the summer of 1916 after accepting 38 American pilots. So, a few months later, Eugene joined the Lafayette Flying Corps on November 15, 1916.
You can read more here: https://en.wikipedia.org/wiki/Eugene_Bullard
For those who might argue that Bullard still wasn't technically a member of the Lafayette Escadrille, it's close enough: There was a real person in the American black pilot's shoes -- both named Eugene -- who faced similar challenges as he does in the movie in a similar fighter pilot squad in France.
It helps to understand that scriptwriters make changes to historical events like this all the time to make for a more dramatically compelling story. For instance, Princess Isabelle of France (Sophie Marceau) was actually only 3-4 years old during William Wallace's military campaigns and, in fact, never met Wallace, as depicted in the hallowed "Braveheart." Compared to that, the change with Eugene in "Flyboys" ain't a big deal.
Bottom line: There's documented truth behind the character of Eugene.