The flagship is the ship the carries the flag. Any ship can carry the flag. Be in charge. Since the flag is more about the ships Captain than the ship itself, but a Captain or Admiral expected to be the supreme commander of any engagement is not going to be driving a dinky little rowboat, but still the better Captain is more important than the superior gunship no matter what Janeway, who is in charge of a dinky little rowboat might say...
JANEWAY: Starfleet Regulation one hundred ninety one, Article fourteen. In a combat situation involving more than one ship, command falls to the vessel with tactical superiority. I looked it up this morning.
If not for that regulation, we'd assume that the guy who looks ten years older than Kathryn would have 10 years seniority in the rank of Captain over her, and should have gotten command of the fleet, but no... Voyager had more torpedoes than Equinox which means that Voyager is tactically superior and Janeway should have promoted herself to Fleet Captain.
Calling Kirks Enterprise a "Heavy Battle Cruiser" happened in Star Trek III, and those same Klingon's where the only people in all of Star Trek to use the term "transfer the Flag" but then considering all the higher ranked officers are called flag officers arn't all ships then flagships?
Maybe "ship of the line" is what you were looking for?