i think the thumbnails should link to a dedicated page for each picture, rather than a lightbox version, like flickr does. that way users can have a url per-picture but still have some context around it (like who took it, show the user's other pictures, promote the 365.io site, etc.) rather than just the raw jpeg url on s3. i'd say add the ability to leave comments and favorites and all that, but it sounds like you're just duplicating flickr at that point.

you could probably accomplish the same thing by using flickr's api. let users upload photos to flickr (with a certain tag that your site would look for) or through your site, but collect and present all of them with your own layout and sharing mechanisms. flickr can host all of the photos and let users keep copies of their own photos in their own photostream. you could pull in comments made on flickr and show them in the same stream with comments left on your own site.

there should still be incentive to use your site to view the photos, though, like having a voting mechanism and some kind of 'picture of the day' that would get displayed on the homepage.