In the pastebin page, these two are a matched pair:
mmcblk0p1-5.1.0
main_kernel-5.1.0
The files at:
http://gitbrew.org/~dasmoover/kindle/touch/forensic/
Are matched pairs for the v5.0.0 "diag" partition. Which should be "good enough".
Although those kernels are not marked, I seem to recall they are the "diag" kernels.
Note that "0p1" indicates the "main" partition and "0p2" indicates the "diag" partition.
- - - -
*nix nit:
The Linux kernel build used by the Kindles is a "modular" build.
Many of the features and drivers are not "built-in" but reside in loadable modules.
The kernel code version and the module code version must match for things to work correctly.
Since the kernel is in the "kernel image" and the modules are in the "system image" those versions must match (to ensure the internal code versions match).