I was hoping that it would be possible to have the app downloaded from the Amazon Android app store, however it is not available there. I realize that it is available from the Google Android marketplace; however that does not recognize the Kindle Fire as an Android device, thus it will not allow me to download it on to my new Kindle Fire.
I know there hacks to get around this but they require either an emulated Android device or another droid. Neither in my case are feasible options, which I suppose would be the same case for many potential customers/users especially seeing as the Kindle Fire is the most popular tablet next to Apple iproducts.
Best Answer
As of June 2012, Ubuntu One Files can be downloaded from the Amazon apps market. Search "Ubuntu One" in the store section. If you enable installing from unknown sources in your settings, you can also install it manually from the project's Launch page. (direct download link)