[Fire HD 8 and HD 10 Q&A, Help & Troubleshooting] kspan:
I couldn't find any instructions for how to deal with replacing the LCD screen/digitizer on a Kindle Fire 8 HD 8th generation device where the motherboard is a little different than previous generations. So I wrote up some instructions to help the next person who needs to replace the screen.

I bought the replacement screen by S-Union on Amazon.

There are two YouTube videos I recommend watching: one on how to replace the screen for Kindle Fire 7 https://youtu.be/_zaQVY2wu58 (I couldn't find one for Kindle Fire 8 HD 8th gen and this was a good enough overview.... any that show how to remove the glass screen are fine) and how to remove the motherboard for Kindle Fire 8 HD 8th gen https://youtu.be/LLujM6w3CA4.

So here's what I did:

1. Remove the back cover. Use the plastic pry tool or guitar pick to wedge in between the side edge of the Kindle Fire and unsnap the back cover.

2. On the backside, carefully disconnect the battery by taking a flat head screwdriver and gently lifting upwards towards your face. The cable you're wanting to remove has little red and white wires and connects to the motherboard at the bottom of the Kindle Fire. See here: https://youtu.be/LLujM6w3CA4?t=90

3. Remove the broken glass on the front. I borrowed a heat gun from a neighbor, but I think I could have just as easily used a hair dryer. I used the heat gun to loosen up the glue around the edges and pry off the old glass with one of the plastic prying tools that came with this kit. I put packing tape over the glass to keep it together. I would recommend wearing rubber gloves, gardening gloves, or oyster gloves to keep from cutting your hands. It takes patience. After removing the glass, you can clean-up any extra pieces of glass and adhesive that get left behind.

4. There's a cable that goes from the LCD screen/digitizer to the motherboard on the back. It's OK if it comes apart in pieces. On the motherboard, there's a 1 cm black square that connects to the LCD screen/digitizer. First, you'll need to remove the yellowish tape covering it and the little ribbon cable. Next, you'll need to unplug the little ribbon cable by pulling the cable out towards the 1 cm black square. Next, take a flat head screw driver and scrape off the black square. It's just lightly glued to the motherboard. See here: https://youtu.be/LLujM6w3CA4?t=156

5. Back on the front, stick only one side of the white double-sided tape adhesive to the edges where the new glass will attach. Later, we'll pull off the top side of the double-sided tape with tweezers so that the glass will stay down.

6. Next, you'll need to remove the motherboard so that the ribbon cable and 1 cm black square from the new LCD screen/digitizer can pass through the Kindle Fire (from front of device to the back). There are four little phillip screws (similar to eyeglass screws) that need to be removed which attach the motherboard to the Kindle Fire. One screw may be covered by a little "S" sticker. See here: https://youtu.be/LLujM6w3CA4?t=53

7. Once the screws are out of the motherboard, you can take a flat head screw driver and pop out the motherboard. Wedge the flat head screw driver towards the edge where the volume and power buttons are and gently press up. Other than the battery and the little ribbon cable for the LCD screen/digitizer, you do not need to disconnect any wires as in the motherboard replacement video. See here: https://youtu.be/LLujM6w3CA4?t=214

8. When the motherboard is loose, just pull it back and pass the cable from the LCD screen/digitizer through the hole where the old ribbon cable went through for the LCD screen/digitizer from the front. Once it's through, you can gently snap the motherboard back into place and put the four phillips screws back in.

9. Practice plugging in the little ribbon cable from the 1 cm black square. It slides in like a plug (there are six pins on top and bottom and they will hold the little ribbon cable in place). Once you see how to reattach the ribbon cable, you can remove it, pull the tape off of the bottom of the 1 cm black square, attach the 1 cm black square to the motherboard, and then plug the little ribbon cable back into the motherboard.

10. Back on the front of the Kindle Fire, remove the top layers of the two-sided tape, remove the plastic film from the rear-side of the LCD screen/digitizer, and push the screen into place.

11. Plug the battery back in. If you bent any pins while removing the power cable, you may be able to gently straighten them with your finger or a flat head screw driver.

12. You can carefully attempt to power on the Kindle Fire by plugging it in or holding down the power button. Please don't touch the back while doing this as you might short out the device and get a nasty shock. If the device powers on, you should hear the start-up beep and see the Amazon logo on the screen. You now know your screen replacement attempt has been successful! If it doesn't power on, you will want to check the connection from the battery to the motherboard and any other cables.

13. If everything worked, power down the device, unplug it, snap on the back cover, and remove the clear plastic film from the front of the glass. Congratulations!