No, they aren't twins. Fili is five years older than Kili. Tolkien didn't differentiate the dwarves from one another nearly as much as Jackson has. In the book, the two brothers have yellow beards, while in the movies, only Fili does, and Kili nearly doesn't have a beard at all.
I've heard that in the Hobbit, though I can't remember at what point, it was mentioned that Kili was actually older than Fili. However, Tolkien apparently revised that later somewhere else, so Kili is officially the younger one.