Hi Issac
There's not a way to download a completed story map to a file like that and reconstitute it. The closest we have is that you can print a Story Map Cascade or Story Map Journal to a PDF file. If you want to host a story map on your own server, it is pretty easy: you just download the source code into a folder on your server then add the ID of your hosted story map app in ArcGIS Online into the index.html file. The maps, data, images etc used in your story map all remain hosted in ArcGIS Online: your server just has an instance of the source code. But if you can't embed a hosted story map in Medium, then self-hosting the story map would I think give you the same result, and wouldn't let you embed.
In this case I would just not embed the story map. Story maps have to be embedded in quite large frames to be usable. Instead you could add screenshot to your post and link to the story map in a different tab. That gives readers the best experience because your story map will fill their display.
Rupert
