This would be more of a use case for blockchain, any site(/user) wishing to mirror the social media would participate in the chain. A post on one site would get pushed into the chain and show up on every mirror.

Media would likely have to be links outside of the blockchain since it isn't usually very good at storing large datasets (it would make it difficult to mirror over time as it grew), so if you wanted a full mirror you would probably have your site fetching media as soon as it is posted and mirroring it yourself.

Or media might be a good spot to integrate with your bittorrent idea. Blockchain handles the distributed state of the site (communities/post text+metadata), and any submitted media is added to the post as bittorrent hashes. I don't know how scalable bittorrent clients are though it might take considerable overhead to seed millions of pictures/videos.