Thanks Adrian Welsh.
We recommend to people authoring story maps that they drag and drop their images directly into the story map. That optimizes the images and ensures they will be accessible to all users and won't be blocked or go offline. With the support we have now in our apps for uploading photos directly into story maps, there's no need to use third-party sites for image hosting. In the case of an image on a site like imgur that you want to include in a story map, we recommend downloading that image to disk and then uploading it into the story rather than referencing it via a URL.
The Story Map apps have built-in support for pointing at images in Flickr and Google Plus/Picasa (although Google Plus/Picasa support is in flux currently and our support for them isn't as smooth as our Flickr support). This support is intended to be useful for individuals and organizations that are already using those to share photos, particularly Flickr. For example if an organization's public affairs department is using Flickr to share photos, then this way those images can be seamlessly and easily used in Story Maps, and that also takes advantage automatically of Flickr's image size optimization. The Flickr workflow also supports captions and geotags stored with the image in Flickr, so it can be very easy to create a Story Map Tour or Story Map Shortlist using pictures in a Flickr album in a few clicks.
Authors can also reference any image on the web directly via URLs, like the images on the imgur website mentioned in this thread. This is useful, for example, if your organization already has images on its website that you want to include directly in a story map. It can also be useful if you want to reuse the same set of images in multiple story maps. However, we don't recommend this approach because the images aren't optimized, so a very large slow loading image will be slow in your story map too. Also some sites might be blocked for some users, like we saw in this thread. And images on the web may move or be deleted.
Hope that helps
Rupert