Just keep trying. It is probably the hardest mission in the game but it is beatable. Pay attention to the order that the ships come in and always go after the oldest ones first.

If you don't want to do that there are mods and trainers out there that alter the difficulty of the of the flak missions and make them very easy. Google is your friend.

I got pretty stuck on the flak missions too, but I didn't want to use a trainer just in case it screwed up any save files I had.

Here is a video of the 2nd Flak mission being completed. Its all about memorising where the ships come from, which is a bit hard to do if you can't actually complete the thing to see the whole pattern.

The flak missions are doable, but you have to be fast about it and know where the ships are coming from.

Also as cogadh has suggested in another thread:

"The MesaMod for the game includes "fixes" that make the flak missions easier, as well as few other cheats like more starting money, faster recharge on shield and generators, cheaper ship upgrades so you can actually get a 10-10-10 ship, etc.

1. Apply the mod and quit out of DSO
2. Copy the save files from the standard game to the mod's save directory
3. Run the game and load your save

Now you can do the easier flak mission. If you don't want the additional "benefits" of the mod, after completing the flak mission, reverse the process and go back to playing the standard game."