It's the "Flagship" because it's your race's first star-faring vessle that you'll use to explore the cosmos with, make contact with alien civilizations etc...
I think it would be kinda neat to designate the "Flagship" and give it some bonuses... But aside from some more hitpoints and maybe a bit more damage, what could you really do? Even after giving ships an individual look, name and exp, their roles are very limited. It's not like you have ships talking to one another or using your ship to make first contact with an alien race.
Hrrm... minor races that are pre-warp and unaware of the Universe around them... hrrm... getting First Contact sort of visions here.