Yes, finally Flickr has added the ability to share your photos on Facebook. Your photos will need to be set up as "public" photos for them to show up on your Facebook Wall. 

Social photo-sharing site Flickr has, at long last, added some much-need social networking integration to its online service. You can now simultaneously post your photos to Flickr and Facebook.

So how does it work?

First, connect your two accounts to get this integration working for you. Once that happens, each time you upload a public photo to your Flickr account, an update will appear on your Facebook wall including the image, its title and the description of the image.

Also remember to shut off the old Flickr to Facebook integration that you may have activated on Facebook. Otherwise you'll see everything show up double! To do this, just go to your Facebook wall and click on Options —> Settings —> Flickr where if it is enabled, just "remove" that enabled feature.