My friend's son had a kid's kindle that wasn't charging any more. They were going to buy a replacement, but then asked me whether I thought it was fixable. Definitely!
I'd not fixed a Kindle before, but my guess was the USB port was probably at fault. Inspecting it under the microscope (and looking at the mouth of the port) I could see it was definitely the problem. It's understandable that a young child isn't always going to connect the USB cable cleanly and the port had eventually given up the ghost.
Opening the Kindle Fire is the process of unclipping the edge - there's no screws on the outside. Once open, the main board can be lifted off, on the reverse side (to my photos) is a ribbon cable that can't be disconnected right next to the USB port.
Using a hot air gun and lots of constant movement, I was able to free the USB port without melting the ribbon cable or the FPC connector (which is entirely plastic). By keeping the airflow moving it protects plastics from heating up but allows the solder to melt, but it takes practise and a careful hand.
Once free, I had a replacement from eBay and once re-installed the Kindle Fire charged up just like old times.
One more bit of tech saved from landfill 💪