Flight Surgeon (or simply Surgeon) was a title held by Starfleet officers at Starfleet Command's Fleet Operations Center, Sol Sector.
In 2143, A.G. Robinson was treated by flight surgeons following his failed NX-Alpha test flight. (ENT: "First Flight")
In January 2155, J.T. Tagamolila, J. Devlin, V. Fredricks, M. Kelly, and J. Billingsley worked as flight surgeons. The title and the officers' names were listed on directory placards. (ENT: "Demons", directories)
Flight surgeon, like many of the other agencies and titles, was a reference to NASA and ISS terminology.