As part of the campaign setup, under building fleets, the rules state. "Each player must choose one ship to be his flagship, and equip his commander to that ship."
Something about the way that is worded makes it seem like it will be your flagship for the entire campaign. Of course the admiral always get to an escape pod if his flagship is destroyed in which case he would select another flagship. I wonder if the intent was that the flagship should remain the same throughout the campaign? That is just an observation really, unless I hear otherwise I will assume that the admiral is just another upgrade.