As far as I know, Flickr has the most complete API of any of the free photo hosting services. (And I know Flickr isn't free above a certain level of use.)
If you know of another photo-sharing service that has that feature, let me know and I will recommend its use as well and will hook it into the occupyweb.org photo flow. To qualify it must have a URL like the one above, and not require an API key, or any programming beyond accessing an RSS feed.
Note that we are creating an archive of these photos, so there is an incentive to a service to support this. Their photos cannot be part of the archive until they do.