Just curious what you mean by "flight control" here? Obviously not helm/navigation. Shuttle bay?
Ah, yes. Authorizing takeoffs and landings from the shuttlebay, launching probes, etc. And I know these duties have also been shared by Ops, on occasion... the TNG writers, as we know, were not always consistent.
(Please also allow me to take this opportunity to observe that Gregory House would indeed make a remarkable Starfleet captain.)