They do, actually. If the public user url is http://365.io/u/2fe9781736, you can access the 20th image by going to http://365.io/u/2fe9781736/20. The link to individual images are shown in the private index view.

Flickr's terms won't allow that type of use of their api. Also, flickr has a 200 photo limit on free accounts that makes project 365 impossible unless you upgrade, and even less so if you use flickr for something else.