Thanks for your help Kelly!
The feature service that stores the images, is one of the layers in the web map which makes up the Story Map. The feature service cannot be shared publicly, which is one of the main reasons I am storing the images in the feature service itself, and not on a public photo sharing service such as Flickr.
Do you know if there is anyway to automatically update the token in the URL so I don't have to update the URL with the new token every 2 weeks? There are probably around 30 pictures in the Story Map. I saw on the ArcGIS blog, where this summer ESRI is supposed to allow uploading of photos directly into web apps which will be beneficial when they release that.
Thanks