I'm trying to select the option Show help center articles when adding a step in Flow Builder but it's disabled. Is it possible in Flow Builder to display articles from a non-public help center?
No, the bot isn't able to present articles if you restrict your help center visibility. An active, public help center is required and article visibility must be set to Everyone.
For more information on this flow step and an example, see the article: Understanding answer flow step types.
For more information on help center access, see this article: Restricting help center access to signed-in end-users.