Will the bolts breaking off make the flare useless? Well, that all depends on how good you are at fabrication.

The flare is set up with a metal ring all around the wheel opening. The bolts you are breaking off are inserted through that ring. As soon as you break that ring, you lose the major clamping source for the flare, and you also create the possibility that the broken ring will wear away paint and create a nice rust spot underneath the flare.
Of course, you may only have broken the bolt. I wouldn't consider that a blessing though, because the flare can now flap against the side of the truck (even if you can't hear it) and wear off the paint.
Two suggestions at this point:
~Leave it alone and trust to providence.
~Finish taking the flare off and prepare to do some work on the metal ring (or hopefully just replace the broken bolts). Don't forget about the screws on the inside of the flare if you decide to take it off.
Good luck.
Camelman