It's not possible yet. The way Flickr integration works is that you only need an API key to add any user. While this may change in the future, currently there is no OAuth authentication, unlike for Facebook source. This is a simpler, 1-click way, but it only allows public content to be shown on your site. Photos marked with private/family privacy option or those that are age-restricted: "unsafe" are not available. Since Flickr offers a very large amount of storage space, it would be widely open for abuse by hosting content privately and for free, leveraging their CDN. It's not what Flickr is for, hopefully you agree.
This FAQ entry was posted in Content sources on June 25, 2015