The files you need to run on a server are in the folder /server. You'll need PhantomJS, imagemagick and pngcrush. You'll need to change the paths of where the files are stored, and set up a cron job to run this file every so often. You should end up with a png that the Kindle can read.
On the Kindle, you'll need to jailbreak it (left as an exercise for the reader), get it working on wi-fi, and set up a cron job on the kindle to read and display the picture from the server. Yo ucan use wget on the Kindle to download the file and eips -g to display it.
See the original weather display that this is based on, and the notes from someone setting it up.
Released under the MIT Licence.