Teleporters and Missiles/Bombs - or better still both!
The Flagship is a dangerous opponent due to its shields and missile weapon - if you don't have any missiles/bombs or a teleporter to bypass the shields and destroy its missile launcher you will be demolished very quickly - since the weapons are self contained once they are out and the crew inside dead the fights get a lot easier
Stage one is the easiest stage if you have enough Missiles/Bombs - simply ignore the shields and target their weapons.
Stage two is the toughest - if you have a cloaking device make sure you use it when the flagship activates its power-surge since you will be quickly flooded by drones - as before you need to get the missile weapon down fast - and the Ion cannon should also be a high priority or beam drones will eat you alive...
Stage three is slightly harder than the first but by now you should have killed most the crew and since it only has 2 weapons left it is a lot easier to "tank" the damage output - simply target the weapons and then you only have to tank the occasional "super weapon" attack
surviving the encounter requires at least 3 shields and a strong crew
while I have heard you can do it without missiles but I really don't see how - you really need at least one launcher to take out the weapons fast or bad things happen very fast... during stage 2 you really need at least one mantis or rock (or have the Engi healing subsystem) as well since a boarding drone is generally one of the flagships weapons of choice... of course level 3 doors can help with that
my favourite ship for the fight is the Federation Cruiser... unfortunately to unlock it you need to first beat the flagship
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