I am trying to use the wikimedia API for wiki commons at:
http://commons.wikimedia.org/w/api.php
It seems like the commons API is very immature
You could try using Magnus Manske's Commons API tool on the Wikimedia Toolserver. It's not an official service, and the documentation seem to be rather sparse (that is to say, almost nonexistent), but the XML output seems pretty self-explanatory.
I can't seem to find the source for Magnus's script anywhere, but I assume it extracts the licensing information from the categories the file belongs to. If you wanted, you could do that yourself: just fetch the list of categories and, if necessary, walk up the category tree until you find a license category you recognize. Alas, the tree-walking part requires either multiple API requests or a database of Commons categories (either live access on the Toolserver, or a reconstructed copy from the database dumps).
Yes, I realize that this answer may seem unsatisfactory. The fact is that Magnus's script seems to be the closest currently existing thing to what you want, and even it's marked as experimental and incomplete. Basically, this is a problem waiting for someone to implement a (better) solution.