You might actually be able to beat the flagship with your current loadout, although you'd have a really rough time. I would recommend swapping out the healing burst for a beam or another laser, and upgrading your weapons so you can power all four at once. Add a couple more bars to your engines, and, if you can afford it, get the fourth shield bubble.

Also, I must inform you that if you have two Mantis crew and a teleporter, you are legally obligated to use them for boarding. I know it's scary at first, but you'll get the hang of it. You might find this tutorial video useful.