So the idea would be that you have an account with AWS (or realistically a more consumer friendly service that's Amazon branded) where all your data lives. Then when you use say Dropbox you can pick "Use my own storage" and grant Dropbox via OAuth the ability to write to /dropbox in your bucket and all your files would live there instead of Dropbox's servers. Lots of the data sovereignty solutions also include a database like interface you can grant apps the ability to use but I can't imagine that catching on initially.

Apple actually already does this with iCloud storage but hides it really well so it feels seamless.