This is just a really quick post to answer some question I keep getting.
1. Download the rom you want and the gapps package if required.
2. Put the files on the root of your sd card.
3. Power off the Kindle.
4. Power on the Kindle keep pushing the power button until the menu at the bottom changes to recovery.
You are in recovery if a curtain comes down that says Team Win
5. Tap wipe, and choose Factory Reset. (This will erase the Kindle)
6. Tap the home button at the top.
7. Tap install, choose your .zips from the right column.
If your rom requires a separate gapps package flash it too before rebooting.
8. Tap the home button at the top.
9. Tap Reboot, choose system.