Even if the homebrew talk app isn't in the amazon store you can add it from your computer and install it (I backed it up from the google store). Worked on my kindle fire.
I've had 1.3.18 running on the spousal unit's Fire HD 8.9 for at least a year, even took it with us to Italy for a couple of weeks. Side-loaded the apk from my 'Droid. Haven't tried (read: "bothered to 'upgrade'") to any of the newer HBT apps because this one actually works great - and is in English...
You may have already figured it out but if you download the 1mobile app from the website it will install a third party market place which has all the google play store apps including homebrew talk.