No, generally it is not allowed to screenshot private stories without permission. This is a violation of privacy rights. Many platforms have measures in place to protect the privacy of users' private stories, and screenshotting them would go against the intended privacy settings.
In most cases, you can't screenshot private stories. These are meant to be private and exclusive to a select group of people. Screenshotting might be considered unethical and could also potentially violate the terms of service of the platform where the private stories are hosted.
Well, typically it's not possible or at least not ethical to screenshot private stories. Think about it. If someone shares a private story with a limited audience, they expect that privacy to be respected. If screenshotting were allowed without permission, it could lead to all sorts of privacy issues, like the spread of personal information that was not meant to be widely shared. And many apps are designed to prevent this kind of unauthorized screenshotting to safeguard users' privacy.