A flagship is usually the most powerful ship of the entire fleet and coordinates the combat operations of its' ships during a space battle. The flagship should be equipped with particularly strong shields so that it doesn't get destroyed easily.
Each empire can have only one flagship at a time.
In battle, a flagship gives a 10% damage bonus to every ship owned by the same empire in that sector.
If there is a Command ship (10% fleet bonus attack and defence) and a flagship in a fleet, all ships gain 20% damage bonus.
Assign a flagship
In order to turn a ship into a flagship, use Flagship command (see Video). The appointment and spreading news of the flagship takes one round ***under investigation***. The flagship then carries the empire symbol on the upper left:
Unassign/change the flagship
In BOTE it's impossible to unassign a flagship. In other words once you have a flagship, it's impossible to not have a flagship unless you get rid of it. You can only assign a different ship to the flagship role though, which frees the previous flagship from its' flagship duty. Once you have a flagship, the only ways to be without flagships again is to scrap your flagship, let your flagship terraform a planet (if it's a colony ship) or build a star base (if it's a transport ship). Or you can lose your flagship in battle, but then you will suffer a huge Morale loss.