Ok, one last update before I focus on cleaning everything up.
I have got the esp8266 connected to the same wifi as the kindle.
I have written the lua for it to send a page turn even to my port running on the kindle.
I had to open iptables on that port on the wlan interface.
Next step will be getting a case for it, with two buttons for forwards/back.
I ended up with the adafruit model available at my local microcenter: mfg link:
https://www.adafruit.com/products/2821