You'll have to cross-compile a git version for the device.
I actually (optionally) ship it on
Kobos, but not on Kindles.
There are a few limitations in place because of its heavy reliance on symlinks, which means it cannot actually be installed in the userstore, and has instead to live in the rootfs, which may or may not be viable on a Kindle.
Also, it's a plain Makefile, so getting the build to do what you want requires
minimal thinking 
.