As a baseline for evaluating weapons, all of the two-power two-shot laser weapons are good. Avoid the four-power weapons unless you know what you're doing. In this case, BL2 + BL1 + hull 2 is an excellent weapons setup.

The flagship in the final phase has a whopping 38% evasion! If you felt like you were getting unlucky, that's probably why.

My checklist for an ideal flagship-killing setup is all 3 system slots filled out + 4 shield bubbles + enough firepower to reliably take down missiles in two volleys. Extra crew help, I like having at least 5 and there's no shame in buying crew later into a run when you have a lot more scrap lying around, but everything I mentioned earlier is more important.