I know nothing about iOS apps. But with Windows I have always had to create an email and then add the pdf file as an attachment for it to work, it does not seem to work if the pdf is the whole document.
Thank you - your reply gave me the clue to an answer: mail-to-Kindle seems to require some email "body" text, as well as the attachment. An email with an attachment, but which is otherwise "empty", is rejected.
So I modified my Shortcuts script to add some body text to the email, as well as the attachment - and it now successfully sends to my Kindle.