Is there a market for this game on Amazon devices?

You are unlikely to find others that have done this on a Kindle Fire on this forum due to relatively small size, if you are looking for confirmation. I did this with my dad's Kindle HD 10 and it worked fine. Fortunately there is nothing "dangerous" or dubious about it. The main thing is ensuring the apks are legit, so you'd want to follow links from a respectable site such as the above. Or google it yourself and pick a trusted site with links.
You can also download them to your computer and use USB cable to transfer them over. Then use DOCS program as a "file browser" of sorts to run the APKs. Just make sure to do them in the right order.