It depends on the settings and permissions of the specific platform. Some allow friends to hide your story, while others might not have that option. Also, it could be influenced by your privacy settings and the relationship you have with your friend on that platform.
To hide your story might imply not wanting it to be known or exposed. Maybe you have personal reasons or fears about how it would be received. It could also be a way to protect yourself or someone else involved in the story.
To 'hide your story on' usually means to make your story unavailable or unseen when it's placed or presented on a specific place or platform. It could be for privacy reasons or to control who has access to it.
Well, 'hide your story on' could imply storing or concealing your story in a particular place or platform. But it's kind of an odd phrase and the meaning could depend on the context.