Mr. Bigglesworth,
Practically speaking, I don't doubt that you can "get away with" having a firearm in your car in the parking lot of a Federal institution in Oklahoma City. However, I guarantee you it is illegal to do so. Pursuant to 18 USC 930: "whoever knowingly possesses or causes to be present a firearm or other dangerous weapon in a Federal facility (other than a Federal court facility), or attempts to do so, shall be fined under this title or imprisoned not more than 1 year, or both."
Let me add some hands-on experience; I served as a Naval officer for twenty years, including many routine Officer of the Day (as a junior officer) and Command Duty Officer (as a senior officer) "watches" on major Navy instillations. As a general rule, Federal -- not state or local -- law applies on US Government reservations, laws are enforced by Federal LEOs, and crimes are prosecuted in the Federal Courts. When, for example, a civil service or military policeman discovered a firearm in a car exiting from a Naval base -- specifically including random "gate checks" for contraband -- the owner was arrested, charged, and brought before a Federal Magistrate (if a civilian) or his Commanding Officer (if military).
This applied to CCW permit holders and it may even apply (local agreements govern) to local/state LEOs. I strongly suspect it would also pertain at Oklahoma military bases, such as Tinker AFB.