Flight Surgeon was a position within Starfleet's Fleet Operations Center on Earth.
In January of 2155, Starfleet officers J.T. Tagamolila, J. Devlin, V. Fredricks, M. Kelly, and J. Billingsley worked as Flight Surgeons. (ENT: "Demons" set artwork)
Flight Surgeon was seen on directory listings seen on the set of "Demons".
, like many of the other divisions, departments, or positions on the listing, is a reference to NASA