Are you using it to mean "Have we completed what we were doing?" If so, it's grammatically correct — and in fact is preferred to a competing construction, "Are we done?"
That said, it's also a bit ambiguous. For a lot of English speakers, especially non-Americans, to be finished means to be ruined, to have no chance of further success. It is primarily an American usage to use it synonymously with to have finished. And even for Americans, depending on context, a sentence like "We're finished" might mean either of those two things. If your business just burned down, you might reasonably look at your partner and say, "We're finished," meaning that you will not be rebuilding the business. On the other hand, if you and your partner have been working together on a project and you've just completed it, you might also then look at her and say, "We're finished."
In either case, the grammar is correct. In the sense you're asking about, finished would literally mean in the state of having completed. In the other sense I've described, it's simply a passive form of finish.