I Iried to get to went to the site to search the Star Trek transcripts site but it wouldnn't come up.
So I went to Star trek transcripts http://www.chakoteya.net/StarTrek/episodes.htm1 and went to "The Menagerie Part 1".
MENDEZ: You ever met Chris Pike?
KIRK: When he was promoted to Fleet Captain.
So the teaser to "The Menagerie Part 1" says that Christopher Pike was promoted to Fleet Captain before that episode. That seems to be the only mention of fleet captain in the episode.
In "Whom Gods Destroy" there is this line:
CORY: Garth. Garth of Izar, a former Starship fleet Captain.
KIRK: No, sir. Captain Garth, Starship fleet Captain. That's an honourable title.
There has been a real naval rank of fleet captain as described by Wikipedia:
So I think that the use of the title "fleet Captain" was probably intentional in Star Trek.