One of the simplest methods to watch Instagram Stories anonymously is to watch them in the Airplane mode. For this method, you’d need to first log in to your account and wait for the Stories panel to load. Then, turn on your phone’s Airplane mode and head over again to the app for the Stories you had wanted to watch.
Once you’re done, you can turn off your phone’s Airplane mode and continue to use the app with a re-established internet connection. Even with the internet back on, your visibility will not get registered in the person’s Story you watched anonymously.