Sigh... I hate to be
that guy, but here I go.
I recently stumbled into this GitHub project located
here along with
this(hardware),
this(TWRP), and
this(uboot) that is for running Android 5.1 on KT3.
With a bit of work, it could be ported to run on other Kindles, but a few modifications need to be made.
Firstly the uBoot needs to be tweaked to boot the boot.img.
Second, a few patches related to Android need to be added to Amazon's kernel source.
Unfortunately, I'm a
bit over my head with this project (being only 15) but I thought I would bring it to the attention of the rest of the community. If anyone would like to work on this I'd be more than happy to help any way I can.
Here's the related
blog post from the author.
Again, sorry for asking for help with something that's beyond my skill level

.