Admirals have adoption of "Flagship" if however they have captaincy experience it's not above them getting their own vessel.
For example, A
Defiant class ship is small and sufficient enough a "Fully dedicated" crew isn't necessary. A ship need only a crew of 50-75 and a skeleton of 30; and a command level officer under captain. Kira, Worf and even Jadzia all took upon missions where command of defiant was relegated to them and crew accordingly.
https://wiki.fed-space.com/images/5/59/Defiant_Bridge.jpg
[Unlike Traditional starships Defiant had no need of a formal "Department heads" associated division of labor]
If you could run a shuttle or runabout, You could run a Defiant.
Ross was in command of Sao Paulo for duration of delivery
Ross:
you are requested and required to take command of USS Sao Paulo. Signed, Vice Admiral William J. Ross, Stardate 52861.3. Computer, transfer all command codes to Captain Sisko.
Now whether than was a symbolic formality or he was actually in command.
In TNG episode "All Good Things..." Riker was in Command of Enterprise, he even had sufficient political clout and power to refit the vessel rather than decommission it.
It's not mentioned how big Starfleet is in manpower or how many flag officers serve at given... Wolf 359, saw 39 ships lose 11,000 people so an average crew capacity for a mid 24th century vessel is 282. Tack on 1,000 to 10,000 running vessels any given time, fleet has anywhere from 250,000 to 3 million under it's employ....of which 1/10th of 1% serve banner of flag officer....If an admiral wants a ship, You give em a ship.
Many Admiral took "Command' capacity of ship when situation demanded
- Admiral Kirk: V'Ger incident 2270's
- Admiral Pressman: Pegasus recovery
- Admiral Jameson
- Ross: Invasion of Cardassia