Don't think DS9 had any "fleet captains", but there's tons of speculation about what Sloan's (fake) rank insignia meant in "Inquisition."
IMO, the "fake" rank insignia is a catchall for various "billets" exercising delegated strategic authority - Sloan was a "Deputy Director" (most likely a Regional deputy, rather than the punative DD for SIA at Headquarters), Sisko could have worn it as COSS-SOL and as Ross' aide, semi-permenantly assigned "commodores"/"task force commanders" not eligable for flag rank could also use it.
By the way, what does a Fleet Captain really do?
I thought (I have no real Naval experience, so, please correct these ideas) Fleet Captains were the Admiral's Aid/Advisor, where the Admiral is over a fleet and the Fleet Captain relays the Admiral's orders to the other ship Captains. He may also be responsible for maintaining day-to-day coordination within/between ships in the fleet. If the Admiral has a flagship, the flagship might have its own regular captain, or does/can the Fleet Captain also have that job, too. Am I over the target?
Whether the flagship has one or two captains typically depends on the rank of the flag officer onboard - commodores did both jobs or had a single "dual-hatted" Captain, vice admirals and full admirals tended to have two (the "flag" (or ship's) Captain and the Fleet Captain, rear admirals depended on mission and availability.
The lack of mention of Commodores in Trek isn't particularly indicative of anything - after all, we get only a single mention of a Vice Admiral in all of TNG, DS9 and VOY together IIRC ("Inter Arma"), and we don't even get to see this guy's pips, but it doesn't follow we should think Starfleet dropped that rank previously and afterwards and only activated it for that episode or season or whatever... And of course obscure background graphics kept referring to Commodores in the TNG era, off focus and all that.
Where we get a bit of confusion is the first year of TNG where somebody with no pips can be an Admiral just as well as somebody with two pips. It's difficult to postulate a flag rank lower than the pipless one! But the no-pip rank might still be Commodore, only now warranting a more egalitarian form of address.
Timo Saloniemi
Actually, Vice Admiral is the only rank that we do know the corresponding pips for, as both Necheyev and Ross (three pipers) are identified in dialogue as Vice Admirals (though they could also be Fleet Admirals ("admirals in command of a fleet) as three pips has also been used for this rank, which logically should have been either four or five pip).
Likewise, I think it's best to assume that Quinn's insignia should actually be a higher one (especially as he was scouting Picard for the two-pip post of Head of Starfleet Academy. However Jameson may have been (semi)-retired or at least exercising a "general portfolio" so warranted "Admiral" merely as courtesy title for a flag officer.
Were there ever any one-pip admirals? That’d be an interesting insignia to see.
I don’t think I’m pro-commodore in the TNG era, but “rear admiral, upper half / lower half” sounds really clunky, lazy, and a little insulting/obsequious. (I don’t care that it’s based on the US military.)
The U.S. Navy didn't start that "upper half, lower half" crap until the 1980s, if I remember right.
No single "boxed pip" insignia has ever been seen in the 24th Century, so we can only reasonably assume that it would be some form of Admiral (given evidence from TMP and TNG s1-2), personally I'm not in favour of RADML as a rank, but would prefer something like Branch Admiral (mentioned a couple of times in licensed media) and/or something like Group Admiral (ala the RW flotilla admiral used by several non-Anglophone navies), possibly depending on billet (staff officers would be Branch Admirals, Rear Admirals and Vice Admirals, fleet commanders would Group Admirals, Fleet (Rear) Admirals and Fleet (Vice) Admirals.