Playing on normal. This is my 35th attempt, but I've only made it to the Flagship several times. The last time around, I got screwed by running out of missiles. So this time around I tried to focus on getting a missile independent weapon loadout. I feel like I have the most solid ship I've had in a while. My four Mantis have max veterancy, as well as my pilot, weapons, shields, and engines.
If you want tips on strategy, we can give you some or you can find the threads where it's been talked about, but for a simple yes or no the answer is hell yes. Upgrading your engine, piloting, or doors systems would help, but as is you're overqualified to take the flagship on.
I need to know if this run was successful! That ship is capable of stomping the flagship, no doubt - it just comes down to the timings and tactics used. (A Heal Burst as well, to keep the Mantis boarders on their feet/talons? Wow.)
If wishes were horses (we'd all be eatin' steak) I'd bump the Cloak up to level 3 for the first phase and get some more Engine power; but that's all just being greedy.
I'd love a 2nd defense drone I, and more engines; makes surviving the missile spam possible. Otherwise, first/second teleport takes the flagship missile-artillery. You don't have a good way of taking out the enemy shields without boarders, and a healing burst can miss if their piloting station is still up.