WordPress.org

The plugin need Flickr API key?

No need, it's included.

How do I authenticate with my account

Through the Settings->Media Flickr menu, click Flickr authenticate, log into Flickr and then click Finish authenticate.

I don't have Flickr user ID. Can I use the plugin?

Yes you can, but this plug in has a function to let you list only the photo of own. If you want to enjoy more, please register Flickr.