2 Burst Laser II, 2 Fire bombs, Anti-ship I, Defense I
Anti-ship drone and burst lasers to take down the ablative shields, followed by firebombing everything. As the crew of the flagship gets more and more beat up, it has less and less crew available to conduct repairs. Just... save your cloak for the special attack (You NEED a cloak).
Using the same scorched earth tactic against the drone controller during the 2nd Flagship encounter also does a lot to negate his attack.
Devs: You might want to give the flagship some exterior airlocks and add the ability to use them for the AI, although I notice none of the AI ships have door control room.
The simple priority list for fighting fires is probably Door control > Medbay > O2

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