Again I do like all of Timo's suggestions above

and I do also think #3 sounds plausible.
Here's another question: if Ent-B ever were the flagship, it does beg a question of "what makes it that special"? I mean, the Constituion Enterprise was going to be mothballed in STIII, so the
name Enterprise evidently meant nothing to Starfleet at the time (and certainly there's no indication in the first three movies - or even in TFF and TUC come to that - that the Connie Enterprises are held in any particular high regard by Starfleet). USS Excelisor would seem to be a more logical flagship too, given its obvious technological advances over the Connie Enterprise. But we all tend to assume that the 1701-B
at least was the flagship of the fleet. It's hard to make the case for the 1701-A being the same as it was really just an old rust bucket that bearly held itself together in TFF, staffed by a geriatric crew who bearly held themselves together in TUC.
... unless... maybe a new Enterprise had been on the cards for a while? The Excelisor project was evidently centered around one ship, but that doesn't mean plans hadn't already been drawn up for a second one (named Enterprise). And maybe the idea
was that this new Enterprise would be the flagship... a refreshing of the Enterprise "brand" with a new crew... while still carrying the great name, and also benefitting from the good publicity of being broadly associated with the legendary James T. Kirk? Without, you know,
actually being commanded by him?

Maybe 1701-B
was the first Enterprise to be a flagship... as a kind of publicity drive on the part of Starfleet Command.