Credit:
To enable this feature, go to www.flickr.com/account?tab=extend and click "Connect".
In case you're worried about privacy, have in mind that only photos that have been uploaded as public (or later set as public) will be shared on Facebook.
If you already use the Flickr app on Facebook for sharing photos between these two services, you might want to turn it off and use this new feature instead, otherwise all your photos will be shared on Facebook twice.