Digging a little deeper, the situation vis-a-vis what rank is what is perhaps worse than I thought as while a variety of insignia have been shown, referencesin dialogue to specific grades above Commodore are limited.
ENT: one-pip flag officers are specifically identified as "Commodore", no personnel wearing no-pips with flag uniform are seen so may be assumed to be the lowest flag rank. Two-pip and three-pip admirals are seen but the grades are not given.
TOS (OS, TMP, KT): Commodores wear the basic flag officer uniform only (as in RN), Cdre Paris' insignia of one broad and three narrow blocks may be regarding as conflicting). No additional information on grades is given in any source, but TMP confirms that 1 additional stripe over the CDRE pattern makes you an ADM (assumed to be RADM but not confirmed). If the KT (sans Paris) is used then the existence of a rank that wears 'flag + 3' or four lozenges (Pike) is confirmed and is outranked by the 'five lozenge' ADM Marcus (Head of Starfleet).
TNG s1 & 2: Commodore may exist as an assignment, but the lowest ranking flag officer wears the no additional pips and is still an 'Admiral' (assumed to be RADM Lower Half, but no dialogue for this). At least two additional ranks exist above this.
TNG s3-VOY: No Commodores were seen or referenced directly, however contemporary officers are familiar with the term. The lowest rank seen is a flag officer with two-pips, no grade given in dialogue, the three pip rank is identified as both Vice Admiral and Fleet Admiral (from the context VADM would appear to be the rank (held by HQ Staff), and FADM a role (held by field commanders), a four-pip rank also exists, however the only grade given for this (Rear Admiral) is clearly an error and admitted as such by the episode's writer Ronald D Moore).
I think that all we can say for certain is that there are at least for four flag officer ranks, sometimes five, and that VADM is the second most senior and the most senior rank always held by more than one individual and is either flag officer + 3 (stripes or pips) or 'four star' which in NATO typically corresponds to OF-9/O-10 (a 'full' General or Admiral).