Hi Allen
Story Maps apps will display whatever symbology is being used in your ArcGIS Online web map (with the exception of the Story Map apps like Map Tour and Shortlist that use their own built-in numbered symbols for point features containing the content for the tours and tabs those apps show users. Apart from that Story Maps simply use the web maps you create in ArcGIS Online.
There are two ways to get a symbol from ArcMap into your web map: a) publish your layers directly from ArcMap to ArcGIS Online as services or b) you can upload your own symbols into ArcGIS Online when you change symbols, so if there is a symbol in ArcMap that you want to use but you don't want to or can't publish your data directly from ArcMap, you can make the symbol as little graphic file and apply it in the web map.
