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Seemingly typical USN acronym, but the the show's writers played a little fast and loose; the correct modern acronym would be ComFAirMed which falls under CinCNavForEur (Commander in Chief US Naval Forces Europe), described here.
But to decipher the acronym they gave . . .
CinC - commander in chief - FAIR - Fleet Air - MED - Mediterranean
This would be the commander of fleet air assets, usually land based, being logistic and patrol aircraft, primarily, in the Mediterranean Sea area, not to include those assets aboard carriers which would fall under CINCLANTFLT.
One can find without looking hard for CINC's
CINCPACFLT - Commander in Chief Pacific Fleet
CINCLANTFLT - Commander in Chief Atlantic Fleet
for FAIR, especially in a WW2 context, as that was when the various Fleet Air commands were first established . . .
ComFAirWest - Commander Fleet Air West (located in San Diego)
ComFAirSeattle - Commander Fleet Air Seattle
ComFAirNorf - Commander Fleet Air Norfolk
etc.
MED is the common USN acronym for Mediterranean, describing the sea itself or as a boundary for operations. When USN ships are deployed to the Mediterranean Sea, it is described in the vernacular as a "Med Cruise".
See Glossary of U. S. Naval Abbreviations
Note that one CinC does not report to another. Nowadays CinC's report to the SecDef and through that office to the President.