Flickr's API is open to the public for non-commercial usage but they require that each application have a unique API key. They use the key for two things: application usage tracking and authentication. The tracking lets them block broken applications and that sort of thing. The authentication allows a user to grant an application permissions on their account without giving out their password.

To do all this you'll need to request an API from Flickr. Once you've got an API key, you'll need to enable authentication. On the list of keys registered to your account you'll see an authentication link. Follow the link and fill in the title and description. Make a note of the API key and secret, you'll need both for authentication.