For my personal taste, I'd prefer:
Commodore of the Fleet (referred to as Commodore) = 1 pip
Rear Admiral of the Fleet (referred to as [Rear] Admiral) = 2 pips
Vice Admiral of the Fleet (formal rank is [Vice] Admiral,
Fleet Admiral is a command billet) = 3 pips.
Admiral of the Fleet (Formal rank is Admiral, assignable as Fleet Admiral [see above], but typically held by HQ Directors) = four pips.
Chief/Grand Admiral of the Fleet (At minimum the
non-substantive rank held by the Commander in Chief but may also be worn by the "Joint Chiefs"*= five pips^
^ A "five pip" braid (and double stripe tunic gilding) was created for the Monster Maroons, but only the latter is apparent on-screen (and exclusive to the C-in-C).
* As the 'five pip' rank appears to be one grade
higher during the Monster Maroon-era than otherwise (as a further "no pip" braid exists in that system), it would be reasonable to assume that the other "Service Chiefs" (In Treklit, originally CoS-UESPA ("Exploration"), CoS-AG ("Defence"), CoS-TSA, CoS-ACSRC and CoS-VSC, but other sources vary) hold Grand Admiral/Chief Admiral rank
substantively during other eras including
PIC).