Wikipedia:
Memory Alpha:A flagship is a vessel used by the commanding officer of a group of naval ships, characteristically a flag officer entitled by custom to fly a distinguishing flag. Used more loosely, it is the lead ship in a fleet of vessels, typically the first, largest, fastest, most heavily armed, or best known.
As far as I can tell, only the nil and the D have been specifically referred to as such. However, other iterations have carried out flagship actions:A flagship was a term referring to the status conferred upon a starship. Typically, a flagship was a vessel commanded by a flag officer (an admiral or similar rank). The term was also properly applied to the ship of whichever commanding officer was in charge of a grouping of ships. A third, more colloquial usage of the term could mean that the ship in question was considered an "exemplar" of the best capabilities and virtues of the force it represented.
The A acted as host to a diplomatic dinner with chancellor Gorkon and his staff while escorting his ship through Federation space, despite being superseded technologically by Excelsior at this point.
The E did the same thing with the Evora delegation, fortunately that went far smoother, as well as earlier taking command of the Federation fleet after the Borg destroyed the admiral's ship during the Battle of Sector 001.
The F was commanded by fleet admiral Elizabeth Shelby during Frontier Day, which as strong a case as any for "flagship".
The two ships that are the hardest to make an onscreen case for due to the very limited information about their time in service are the B and C, though in theory they do qualify by virtue of being "typically the first (no), largest (yes), fastest (yes), most heavily armed (yes), or best known (HELL YES)".
Because it predates the Federation, the NX-01 by definition does not qualify, and the G... the less said about that, the better.