Hi Amy,
Unfortunately there isn't a solution for that right now, but we are thinking about how to support this in the future as web technology advances to support this. Since story maps can have so many different types of dynamic web content, this is not an easy requirement to address. We'd also have to determine how/if we could support content like YouTube videos, copyrighted images, etc. that might appear in the Story Map.
It might be helpful if you could please add your idea to our ArcGIS Ideas site so others could vote for it and add their thoughts.
For now the best way to do this would be to take screenshots and/or record a video walk-through of the story map.
Owen
Owen Evans
Lead Product Engineer | StoryMaps
