Flickr is a hosting site, so Flickr doesn't own the copyright to any of the photos published on there. Individual users who post the photos dictate their own terms, which then appear under License in the bottom right of the main screen for each photo. Of course just because someone claims to own the copyright to an image they post on Flickr, it doesn't mean that they are actually the genuine copyright holder or that by making the claim on Flickr it somehow supercedes or invalidates the original copyright. You'll find thousands of photos on there posted as "all rights reserved" which you can be 99% certain don't belong to the person who's claiming that right. As Alan said, it's still up to the original copyright holder to take action on infringements if they think its worth it.