I have a Amazon Fire 7 9th generation. Amazon's app store is void of key chess apps. See my article on installing Chess.com on a Fire 7 (click here). Today I installed Lichess and Aimchess apps on my tablet.
First you will need to install an apk downloader in your browser (Google's Chrome).
Also I use Dropbox to transfer to the tablet. Dropbox is available in the Amazon App Store.
Find the chess app in the Google Play store. Run the apk downloader. Select your device configuration as close as you can. Download it to Dropbox.
Open Dropbox on your tablet and run the apk. You may have to try a several versions to find one that works. I had to use Aimchess version 1.3 instead of the latest 1.7. I don't know the difference. I think they are just a way of connecting to the website anyway.So I've installed Chess.com, Everyman Chess Books Viewer, Lichess, and Aimchess using this method. They all work on my tablet. I hope this helps someone. Be sure to follow the blog if you like the content. Also let me know if you have another technology issue. I'll try to find a solution.