With Admiral Kirk in command of the Enterprise for the V'jer Incident would I suppose make her a flagship as it would be holding the flag of a Starfleet Admiral (regardless of the oddity of him being "reduced" to Captain and Decker being "reduced" to Commander). It would technically be a flagship of Admiral Kirk until its destruction, even with in under the command of Captain Spock. It was running as a training ship in 2285, but it seemed like they were preparing to put her back in full service with a new crew until she returned from Genesis and told she was to be decommissioned.
After that, the next Enterprise is just a ship under command of Captain Kirk.
The Galaxy-class USS Enterprise is called "The Flagship of Federation" more than once. Though Picard is not a flag officer, he has been offered positions that would likely hold a flag rank. He is also likely one of their senior captains. If they still had the rank , he would probably be a Fleet Captain as oppose to a Rear Admiral or Commodore.
The Sovereign-class, Enterprise may also be a "Flagship of the Federation" given the role it seems to take in diplomatice functions. Though we see it so little we cannot be certain of this. They did seem to give Picard a new ship as soon as it was finished and named it Enterprise as quickly as possible following the loss of the Galaxy-class vessel. Where as when he lost Stargazer, he seens to have been grounded for eight years. Though in truth we don't really know what assignments Picard had between 2355 and 2363.
No clue on the other Enterprises. Archer's ship was not the flagship, though for a while it was the only ship that could go out that far, that fast. It might have been a flagship at the end of its career in 2160-61 if Archer was promoted to a flag rank due to the Romulan War.
After that, the next Enterprise is just a ship under command of Captain Kirk.
The Galaxy-class USS Enterprise is called "The Flagship of Federation" more than once. Though Picard is not a flag officer, he has been offered positions that would likely hold a flag rank. He is also likely one of their senior captains. If they still had the rank , he would probably be a Fleet Captain as oppose to a Rear Admiral or Commodore.
The Sovereign-class, Enterprise may also be a "Flagship of the Federation" given the role it seems to take in diplomatice functions. Though we see it so little we cannot be certain of this. They did seem to give Picard a new ship as soon as it was finished and named it Enterprise as quickly as possible following the loss of the Galaxy-class vessel. Where as when he lost Stargazer, he seens to have been grounded for eight years. Though in truth we don't really know what assignments Picard had between 2355 and 2363.
No clue on the other Enterprises. Archer's ship was not the flagship, though for a while it was the only ship that could go out that far, that fast. It might have been a flagship at the end of its career in 2160-61 if Archer was promoted to a flag rank due to the Romulan War.