Here is how I recommend using cloaking:

On phase 1, it really doesn’t matter too much, higher level cloaking just gives you more time to charge weapons, repair, board, etc. I haven’t really found a reason to not use it unless your cloaking gets hacked. If there is anyone who knows better, correct me if im missing something.

Phase 2, level 2 to 1 is usually all you need to dodge the surge, just make sure your cloak ends as soon as possible once the drone surge is done. You can usually insure this by firing weapons to break cloaking. Level 3 cloaking is also nice to dodge missiles and the drones.

Phase 3: For phase 3, I basically always like to use level 3 cloaking. The strategy I use is i wait for the missiles to fire, drop shields, and wait for the missiles to almost hit my ship before i cloak at level 3. If you dont fire weapons, you should be able to dodge the missiles and flagship power surge in one cloak. Keep in mind that this isnt 100% guaranteed to dodge, but also keep in mind that this can also be done with level 2 cloaking very rarely. Its just random. Once you break flagship missiles, its better to drop to level 1 cloaking to avoid each surge afterwards.

Hope this was helpful :)