You should just be able to paste in the URL to your image. Make sure that URL works in a separate web browser tab first, and that it ends with a file extension, like .jpg:
https://downloads.esri.com/blogs/places/sandiego/mcasd_la_jolla_large.jpg
https://downloads.esri.com/blogs/places/sandiego/mcasd_la_jolla_thumb.jpg
If it still doesn't work, you could paste the URL into this thread for us to look at.
We actually recommend uploading images directly into story map apps rather than referencing them via URLs. See this FAQ about image sizes for the Story Map app you are using: Frequently Asked Questions | Story Maps
Rupert
