What I think With that in mind, I feel this concept is very close to a lot of the p2p or decentralized content distribution systems being tested out these days, like aether[1] or matrix.org[2].
The backend implementation that matrix.org uses is rather ideal. It's Federated JSON over HTTP(S). The clients out today are heavily focused on chat, but it is data agnostic. You could have client that writes rich media content and a client that displays this as a blog. Going back to the streams concept, you could have a client subscribed to multiple streams (rooms in matrix vernacular) and as people post their messages - rich media or simple "how are you" comments, it would get federated out to each home server, which can present a web client interface like in tonsky's mock-ups.
For the concept of amazon providing sensitive order information as a stream/matrix room, there would have to be an add-on concept built into the client of some sort of security token. I'm not talking about a losable gpg keypair, but something amazon generates and provides to you (like they do with their AWS services already) Amazon would then create a personalized stream for you, using that security token to encrypt. Since amazon provides the content and the key, they can replace your key at any time.
[1]: http://getaether.net/ [2]: http://www.matrix.org/