Unbroken isn't on Netflix yet unfortunately. It was actually only released in the US on Christmas Day, so is still showing in movie theatrers at the moment.
If you want to wait to watch it at home, DVD releases generally come 3 months after cinematic release. Following this, the time taken for a movie to appear on Netflix can vary depending on financial considerations and who own the rights to the content (the reason that some movies are not available at all). They have said in the past to think of Netflix as a channel showing a range of movies, rather than a library of any movie ever made.
With this in mind, if you really want to see Unbroken, I wouldn't hold your breath waiting for it to appear on Netflix... Incase it doesn't!
In the meantime, here's a trailer for you:
