Robert Comsol wrote:
Personally, I've taken this as a hint that during TOS the Lexington
is the flagship of Starfleet. This brought me to the next question, i.e. is there some kind of Starfleet tradition honoring the (current) flagship.
IMHO, the previously most accomplished starship is honored by adopting its insignia as the Starfleet uniform insignia for a period of something like seven years or so.
Hence, the Starfleet flower is the insignia of the Starship Lexington
and Bob Wesley has been and still is its current commander.
I think a simpler explanation would be that when the commodore is acting in the capacity of a flag officer, commanding multiple vessels, they wear (or have the option of wearing) a badge that reflects that level of authority.