The source files for the Classic StoryMaps templates are available for download and customization. The source files are not available for new StoryMaps.
The Resources page on the Classic StoryMaps site states under the If You're a Developer section (located at the bottom of the page): "The Esri Story Map app templates are open source and are available on Github. Free ArcGIS Online accounts are available to developers."
Links provided are the following:
Classic StoryMaps are not available offline but a couple of templates offer the option to save to PDF .
The new, updated StoryMaps is only available through the builder in either ArcGIS Online or Portal. The source files are not available for download.
A PDF of the StoryMap can be saved by clicking the three dots menu at the top right of the story, and clicking Print preview.