Hi Mat,
Story Maps let you embed web content from a web page or iframe, so you can use any charting/graphing web service that can be shared in these ways. There are a lot of options out there for developers and non-developers.
Soon Esri will be releasing it's own graphing tools in the forthcoming Insights app and we'll be working to incorporate Insights charts into story maps in future releases.
Insights for ArcGIS | Esri Video
ArcGIS Analytics | Esri Video
Owen
Owen Evans
Lead Product Engineer | StoryMaps