It would be worth looking at the
DIY Kindle voice control (simulating key presses) thread. Ignore the voice recognition stuff! That thread has the basics of fully controlling a kindle via emulated key presses over WiFi or USB (USB network mode). As the kindle will need to be powered anyway if sleep is disabled, USB is vastly preferable.
As Dsmid pointed out earlier, probably the easiest way to implement the host computer that controls the kindle would be to use a
Raspberry PI. It has enough I/Os to handle the switch interfacing required. There are many other embedded USB hosts that would be suitable but IMHO they have much steeper learning curves than a PI and with their development tools, are likely to be less cost effective for a one-off project.
On the Kindle side of things, you are probably looking at a K4 (non-touch) as all functions are accessible with only 9 buttons and controller directions to emulate.
If there is an existing accessibility device in use that has a serial output and the facility to add additional functions, it may be possible to do without the PI, by interfacing directly to the Kindle serial port and writing a daemon to directly interpret the serial accessibility control stream, but that would require hardware mods to the Kindle to bring out the serial port and add level converters, and IMHO it is better from a long term support and reliability point of view to keep the kindle 'vanilla' apart from software hacks so a replacement device can easily be substituted.