The answer is to have cloaking upgraded to level 2 before the flagship (you should do that as soon as you can anyway after buying cloaking), so a 1-damage missile hit doesn't break it. Level 2 cloaking is really great in most fights, but against flagship phase three you only need 1 level worth - you want it to recycle faster to dodge the laser surges (they aren't delayed while you're cloaked, unlike regular weapons), so the extra level now acts as a buffer against damage.
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FTL - Faster Than Light
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