Hi Sian -- I'm sorry you're having an issue with your swipe app. My Stories should flag any sharing issues, but to be sure you can double check the sharing not only on the web maps that are used in the swipe app, but also any layer items in those web maps (such as that hosted feature service you mentioned.
Also, are any layers in the story subscription or premium content layers? Those can sometimes prompt for authentication if they are not proxied correctly.
Owen Evans
Lead Product Engineer | StoryMaps