No you can't do flashpoints together, BUT... Evidently Empire and Republic must have some of the same world missions. A Jedi and my Sith Inquisitor had the same mission which we did togetther. We did not try to kill each other, lol. BUT.... our 2 companions kept getting into it from time to time. We could not stop them. We just had to wait till one died. (I was higher level so his died when they fought). It was a fun run and very different. The companion fights were actually pretty funny.