Okay, I finally made the connection and figured out how to create more Task Forces. So I've got this task force, "3rd Fleet" with two TGs under it, the "3rd Cruiser Squadron" and the "3rd Support Squadron."
In the 3rd Cruiser squadron there's one ship, the Ulysses S. Grant, that's got a flag bridge. That ship's CO is Commodore Brian Dunn. The Task Force's commander is RAdm Ewan Newman.
Newman is on Earth. Dunn is on his ship, also in the Sol system. On the Task Groups window, in the History/Officers/Misc tab, Dunn is listed as the Senior Officer in system, and Newman is listed as the Task Force commander.
My question is: What's the flag bridge doing for me? Is there some way to move the TF command staff onto that flag bridge so that they'll travel with the fleet?