I only just now had time to try and check it out. I had it delete the old one and redownloaded, no luck.

I removed again, and went to Android Settings to clear the Kindle app cache.
This time the dowloading screen seemed more obvious, but no extra chapter.

Now, I didn't see a chapter entry, but I went to Galvachren's Guide and back-paged, and still no joy.

If the information helps, I'm using a US account.

If anyone figured this out, or magically got it to work and has a theory, please let me know!

Edit Oct 26/20:

I finally got it. I found it in my Kindle library and "remove[d] download." After which I clicked to open it, making it download again.

It finally showed up!

Thanks to /u/Exfiltrator for asking.
I'd personally given up, but went through the motions just to be able to give a reply so they wouldn't feel like they were talking to themselves.