Wouldn't there be anything in Flickr's ToS that would prevent third party developers from hosting their app's photos there? I like the suggestion though.
Yes. From Flickr: "The direct link to a photo file is no longer shown on the page. Per the Flickr Community Guidelines "pages on other websites that display content hosted on flickr.com must provide a link from each photo or video back to its page on Flickr." Linking directly to the photo file doesn't do this."