It's about time for a new post since a lot of things have changed over the course of the past four years.
First things first though, the good news is there's finally an almost official way to properly use the script with your Amazon Alexa. Luckily all major home automation projects became inspired by the idea of the original script and some inner workings have been discovered by people smarter than me. Michael Geramb of openHAB and Ingo Fischer of ioBroker came up with the idea to proxy the login to Amazon very similar to how a mobile app would.
The result was for example the nodeJs package alexa-cookie2 (by Ingo Fischer). Looking more closely at the result of the login process it became clear that only a single item is required for our purposes. Hence I created a small nodeJS app that will output the token after successfully completing the login.
As not everybody would want to install nodeJS (or run it in Docker) I created packaged binaries using the nodeJS packager pkg.
While the old login flow may still work (for some time) I strongly encourage everybody to try the new cleaner method.