You do not have to have the flagship for a bonus inherently. However, the flagship counts as 1 ship. So, if you have both portions of the flagship, that counts as 1 ship, not 2. I feel like the quotes I made answered that question very specifically. Maybe it didn't though.
I know from experience, you do not have to have the flagship. If you do, it counts as 1 ship, not 2.
