From the Stripe dashboard I can view a receipt (click preview link in invoice details). The receipt is then shown inside a popup but there is a permalink in it, so it can be viewed as a separate page. The URL of an emailed receipt looks like this:
https://dashboard.stripe.com/emails/receipts/invrc_xxxxxxxxxxxx
This URL does not require authentication, and so would be perfect for allowing me to show links to receipt details from inside my app's billing page. Except that there seems to be no way to get the magical invrc_xxxxxxxxxxxx id from the API, so I am unable construct the URL.
Or for some strange reason, Stripe engineers went through the trouble of designing an unauthenticated receipt view page, but have decided not to expose it via the API. Why??
This issue has been brought up in Stripe API - Receipts Listing (see comments section at the bottom), but no explanation, solution or justification was provided. Hope this more specific question can help.
UPDATE: As of January 17 2019, this is now possible to do. The Charge object has the receipt_url property that lets you access this information whether an email receipt was sent or not!
That's unfortunately not something currently supported. There isn't any way through the API to get an receipt ID to be used here. That endpoint was built with the intent that it would only be used to permalink to a receipt from the body of a receipt email. That said, we are considering building out this functionality at some point in the future.
EDIT: Looks like my colleagues in Stripe support beat me to the punch here.
UPDATE: as of 2019-01-17, this is now supported via the receipt_url property on Charges (https://stripe.com/docs/api/charges/object#charge_object-receipt_url).