Found the solution, described here: Flickr Image URLs
You can construct the source URL to a photo once you know its ID, server ID, farm ID and secret, as returned by many API methods.
The URL takes the following format:
http://farm{farm-id}.staticflickr.com/{server-id}/{id}_{secret}.jpg
or
http://farm{farm-id}.staticflickr.com/{server-id}/{id}_{secret}_[mstzb].jpg
or
http://farm{farm-id}.staticflickr.com/{server-id}/{id}_{o-secret}_o.(jpg|gif|png)
You can find examples and image size prefixes as well on the source page.