Hi Chad -- Sharing to a group isn't currently supported by story map builders, but you can do it manually.
Go to your Content page in your ArcGIS account and check a box next to one or more of your items you should see the option to Share at the top of the list. If you don't see it after checking at least one item you must not have permissions to share items and should contact your administrator.
Once you confirm that you can share items, you'll need to share the story map as well as any maps, scenes, and layers that are used in the story to the group you've created. When sharing to group, none of these items are shared automatically.
Owen Evans
Lead Product Engineer | StoryMaps