I don't have a Kindle Fire HD, so this may not help.

I understand that the kindle fire tablets don't have the Google Play Store , and use the Amazon Appstore instead. If I understand correctly it is the same one you can download for an Android smartphone or tablet. I shearched for Firefox in that appstore and it seems it is not there.

It would be a good idea for Mozzilla to allow apk download so the people that for whatever reason don't have access to the Google Play Store can still use it.

You can try manual apk install however Release and Betas installed manually will not update. http://download.cdn.mozilla.net/pub/mozilla.org/mobile/releases/latest/

The reason why there is no Firefox on Amazon Appstore is not due to Mozilla (as they want it there even) but due to Amazon's practice of modifying and resigning the package and causing update problems as a result. Which has not been resolved since Firefox 9.0 was submitted an then removed shortly after.

For reading as Bugzilla is not a discussion forum like here. Bug 690791 - submit Firefox to the Amazon Appstore Bug 713777 - Amazon modifies and re-signs apk after uploading [was "Cannot install Firefox from Amazon appstore if Firefox Beta already exists on device"]