I was running Kali linux on my Raspberry Pi, but never on a Kindle. This looks interesting:
http://docs.kali.org/development/kali-linux-arm-chroot
Not sure what kind of vulnerabilities could be exploited over a kindle wifi connection, but they may well have more than a few vulnerabilities, being based on old versions of some tools in their rootfs. Based on what I have seen in my meager exploration of kindle internals, kali linux is worth a shot, as a tool to explore and test various potential gateways to rooting a new "locked down" kindle, to figure out how to jailbreak it.