I've never worked with the older Kindles but there's a few tips I can pass on from working with the KT2 - there's a good chance that not all of these will be applicable to your device:
- Compile one of NiLuJe's toolchains (the version compatible with your device) and try to build and load some kernel modules before flashing a full kernel - doing this will give you some confidence and allow you to verify that your toolchain works correctly before you do anything that will be tricky to recover from
- Backup everything before you even think about flashing a self built kernel; you will thank yourself later if things go badly wrong
- It's a very, very good idea to have a serial cable permanently attached to your Kindle when messing around with the kernel + rootfs - it's likely that you'll brick your device at some point and being able to access it over serial will make life a lot easier
- If you're starting out, you will probably find it easiest to flash a new kernel using fastboot -
you can enter fastboot mode from bist or by using the magic key+MfgTool+custom uboot combo (IIRC this is pretty much how Kubrick works)
- If the ancient kernel version on the DX supports the g_file_storage or g_multi kernel modules, you can directly flash your Kindle with dd without needing to enter fastboot in the first place
Once you've got your toolchain set up and have flashed a few custom kernels successfully, the process is a lot less scary. That said, the real struggle that you're going to face will not be running your own kernel - it'll be tweaking your chosen userspace to allow you to load the firmware blobs and waveforms required by the wifi/wan hardware + screen. Like NiLuJe said above, it's possible to run an Alpine Linux userspace within a chroot (or as a rootfs if you mess around the init scripts first), but you might be disappointed with how slowly it runs and the amount of additional work that'll be required to get all of the hardware vaguely working.