If you go to
https://xdaforums.com/t/guide-instal...eader.4450117/
You can see how to install android on kindle. Well thing is, even though you try to install, your kindle is too new to install. The project only supports kindle which has the bootloader unlocked (pw1,2,3, basic 7,8, etc.). And that is your pw4 has the bootloader locked. So no it is not possible.
TL;DR
No, not possible