@dpavlin: Yifan's writeups on this are
here (building) and
there (patching the update/recovery).
Seaniko7 also did some stuff with Kindle kernels,
here for example.
And
here's a small patch for the 3.3 kernel to at least *build* on a recent system.
If you intend to flash *everything* (kernel + modules + support files), I think any (working
) toolchain will do, but if you want to mix & match, you'll have to use something mostly matching Amazon's TC (twobob might steer you in the right direction here, he's done it
).