Kindle Fire runs on Android, so I don’t think there is any extra programming stuff to be done (bearing in mind I know precisely zero about any of these processes)…
It’s just that they have a separate App store and you can’t get anything from the Google Play store on Kindle without doing things you’re not meant to… I assume for developers it just means submitting an already completed Android build to their store for approval…
The Wadjet Eye Games and things like Simon the Sorcerer and Broken Sword are all on the Kindle store…
I will happily buy the game a second time to play it on Kindle!