I think that the Custom Facebook Feed plugin publishes the feed using the WordPress ‘page’ post type. If this is the case, it should be possible to publish the pages created by the plugin to Discourse by adding page to the plugin’s “Post Types to Publish” setting. That setting is found on the plugin’s Publishing options tab.
If this works, you could publish the feed pages to a protected Discourse category that is configured to only allow members of a particular group to access it.