I don’t see a URL scheme (ref. the platform knowledge base), but it does look to support Siri in version 4.4. With any luck, after triggering the sleep story via Siri a few times you’ll see a donated action in Shortcuts for it and you can just drop it in to your custom Shortcut.
The reference to Siri is in the link provided and provides an example of how to trigger a sleep story which is what you asked for.
Once you have done this “several” times (the exact number depends on the whim of Siri), check if you have the action in your Shortcuts Siri actions.
If you do, drag it into position in your custom Shortcut.
Alright. So I need to just need to wait for it to pop up with a sleep story once in a while and then when I’ve done it enough times, it will appear as an option, right?