IM not sure if cloud is the solution to you. The cloud is where network services such as file storage and server hosting take place. I think the apple icloud is pushing your internet, apps, etc to the internet. Amazon has a similar service for the kindle fire, where you can upload music to their servers and stream it at your leisure. It may take care of your file transfers, but I doubt it would give you the apple updates.
I wonder if this article will help you do a file sync. It looks like a lot of work to get something so simple done..... Debian instructions, but should be very similar for lmde. http://wiki.debian.org/iPhone
Other than that Im not sure where to point you.