You can, but if you soft brick, you will need a fastboot cable to revive your Kindle. Make ONE mistake and that'll happen. After you flash the bootloader, boot.img, and the recovery.img, there's no turning back until you've flashed a rooted ROM or a fastboot cable. So: when you get to the blue screen, you have one chance to enter recovery, or you will soft brick. I reccomened pressing the power button multiple times when it prompts you to enter recovery. Once you're in TWRP, you CANNOT reboot until you've flashed a custom ROM, or you will soft brick. So, unless you have a custom ROM installed already, there's no point in using TWRP's backup system.
Use
theese drivers to get your ADB/Fastboot drivers installed. (Assuming you have Windows), and enable ADB Debbuging in Settings>Security.
If you haven't already, ROOT YOUR DEVICE. I recommend Root w/Restore by Bin4ry. Use the Old method (download
here)
Next:
BACKUP EVERYTHING!!!!!!!!!!!!!!!!!!!!!!!11 You will not be able to go back and do any last-minute backups after this.
Then, search Google for Flashify, and install the .apk) Open it, give it root permisions, tap the 3 dots on the top right, and choose "Reboot bootloader". Tap it once more and then your Kindle (hopefully) will boot into fastboot mode.
Make sure your fastboot drivers are working.
Use
theese three
files and
this thread for instructions on installing the bootloader and TWRP. Ignore anything that mentions stack override, backing up, and fastboot cables.
Once you're in TWRP, keep your Kindle plugged in and find a ROM. Grab OpenGapps pico for your specific ROM version too. Grab
this to gain root. ADB push those to /sdcard/, factory reset, wipe /system, and flash all 3 zip files in this order: 1. ROM 2. Gapps, 3. SuperSu. Reboot & enjoy.