According to this thread:
https://wiki.mobileread.com/wiki/5_x_Jailbreak a Kindle running Firmware 5.8.x and up will not allow Jailbreak. The current firmware in my PW3 (G090 G105) is version 5.9.2.0.1. Can anyone verify if my device can be jailbroken and if so, where to find the downgrade file that works?