Originally, starship personnel (in contrast to starbase personnel) had the
Enterprise's insignia.
Then, all Commodores and Admirals and Starbase personnel wore that "flower" insignia.
But then, it also became the insignia of the
USS Lexington (that's the only starship we've seen that has this insignia).
Notice Commodore Wesley's high command chair (neither
Exeter or
Defiant had this chair), looks like the
Lexington might be Starfleet's flagship (in the mirror universe,
ISS Enterprise apparently is the flagship there)
Bob