Were you able to solve your issue with the fonts? I'm having the same issue but only when I go to publish the epub on Kindle Direct Publishing. When I view it through their previewer none of the fonts display. It seems like they display the default Kindle fonts. If you found a solution, please share
moved to InDesign Epub forum.
The Design Truth:
I spent a ridiculous amount of time trouble shooting the issue, it was months ago when I finally resolved it and because there was no discuss or reply in this forum I completely forgot I posted here. Too bad this forum was not more active as I probably would have remembered and posted what eventually solved the issue for me.
Sadly, I don't have an answer for you: I'm just pointing out that InDesign is designed for producing EPUB. Amazon's file formats are completely proprietary and they aren't always well documented. Have you asked in the Amazon Publishing forums?