[Kindle Fire General] kinfauns:
Symptoms: The Kindle Fire starts booting normally, but then shuts off prematurely or reboots spontaneously before the device completes the startup process. In extreme cases, the bootlogo may not even appear on the display and only the power switch LED lights up before the device shuts off again.

Cause: The battery has been depleted to the point that not enough power gets delivered to the CPU. The CPU detects the low power condition and its safety features power off the device.

Solution: Use the stock 1.8 amp AC charger to recharge the battery. In most cases, this seems to be enough to get power to the CPU and battery that it will begin to charge again.

In some rare instances, not even the AC charger will be enough to charge the battery. Why? The Kindle Fire's hardware does not have the ability to charge its battery offline. The device needs to be up and running so the ramdisk can handle the battery charging operation and that requires the CPU to be powered up. If the battery cannot provide enough power to the CPU, it shuts off automatically and the boot process stops or restarts... a classic catch-22.

Devices without FireFireFire 1.4 (or later) will need to upgrade to that version. This bootloader stops the boot process for a low battery condition (less than 3%) and charges the battery to its specified minimum before continuing to boot.

If the device has an earlier version of FFF, use the temporary fastboot mode feature to fastboot flash the new version using fastboot. If the device is using the stock bootloader (white/orange "kindle fire" bootlogo), a factory cable is probably necessary to put the device into fastboot mode.

Although the preferred method of installing this bootloader is through TWRP, it is dangerous in this situation because TWRP could shut down without warning. Because of this potential for a premature TWRP shutdown and a bad flash as a result, fastboot must be used under these circumstances. The device can be powered entirely from the USB port while running the bootloader, so it's much safer in this regard. Be sure to check the MD5 sum of the distribution, extract the contents of the zip archive and find the binary inside the cache directory. Flash this file using fastboot.

Using an older version of FFF...

fastboot flash bootloader /path/to/u-boot.bin
fastboot reboot

With the stock bootloader...

fastboot -i 0x1949 flash bootloader /path/to/u-boot.bin
fastboot -i 0x1949 reboot

Note: In both cases above, the "/path/to/u-boot.bin" must be replaced with the actual path to the file's location.

After a reboot, the bootloader will automatically stop the boot process and begin charging. The backlight is normally off in battery charging mode to conserve power, but press and hold the power button for a few seconds and a battery charging notification will appear on the display.

Note: Currently, neither FFF 1.4 nor 1.4a will display a bootlogo before entering battery charging mode, so the device may appear to be bricked. Press and hold the power button for a few seconds to display the battery charging notice. In addition, these versions will only enter battery charging mode when hooked up to USB power and not the AC wall charger. The developer is aware of both situations and has indicated that he intends to implement fixes for these issues.

Credits

pokey9000 - For providing information about the Kindle Fire hardware

SBlood86 - For sharing his experiences and initial ideas for a fix

Hashcode - For fixing/implementing battery charging on the bootloader​