You'd probably need a VPS to do that. What you could do is have it pull files based off a database on the server, stick them in a cache, then convert them to what they really are (I assume the utility in the OP just adds a PNG header, so the VPS could just strip that) and then stream it.

Maybe you could hack it together with owncloud or something? I'm sorta tempted to try doing something like this but I don't want to screw flickr over.