Hi Sara -- the team is considering adding some basic widgets like basemap pickers and time sliders to the Story Map apps in future releases, but until then you can still get the behavior you are looking for by embedding one of the ArcGIS Online configurable apps in your story map. See this blog post for details on how to do this.
You can embed any of the configurable apps like Basic Viewer or even a Web AppBuilder app in your Story Map to allow your audience to swap basemaps; however, be mindful that providing too many functions can be overwhelming/confusing for your audience so be sure to use them only when needed and consider explaining how to use them in the text of your Story Map.
