On the Story Maps team we are sort of big fans of static images of tables, charts, etc because they let authors get exactly the look they want. You can find some nice examples of how people are presenting this sort of data in the Story Maps Gallery for the Cascade app, but you may have already browsed that. In a Cascade you can also 'animate' your static tables and charts by using immersive sections to display a sequence of static graphics, You can also make really long charts and tables that readers can scroll through (for example, see: Living in the Age of Humans
Story Maps don't support dynamic tables and charts that for example, reflect queries and selections on a map, because the idea with story maps is that you can tell the story without too much user interaction, except for them to advance through or pick places or tabs they want to view. It is possible to embed third-party web content into Story Maps so, for example, if you can create an interactive chart on the web, you may be able to embed it into a story map (if that web content allows itself to be embedded, not all does). Or you could use a different ArcGIS app and then embed it into a Story Map, or link to it from your Story Map for readers who want to delve deeper. However in general I would personally try and keep things simple and refine a story so you don't need those extra elements.
Rupert
