Hi @stingpin
It appears as though the digitizer (touchscreen) is faulty.
Here’s the Ifixit Kindle Fire Front Glass Panel Replacement guide that shows how to replace it.
The problem with Kindles is that you have to know the exact model number so that you can get the correct replacement part, as they aren’t all the same, even if they have the same model name but are a different generation.
Here are some links that may help to identify your particular model/generation
link 1 scroll down and click see more on the first answer Toggle navigation How to identify your Kindle model: serial numbers, features, look up … Benjamin March 5, 2019
link 2
I realize that both these links require you to use the tablet and that you can’t navigate through the tablet BUT you can use an OTG cable (supplier examples only) and connect a USB mouse to the cable and connect it to the tablet and use the mouse to navigate through the tablet. Be aware that the mouse will be powered by the tablet’s battery so given that it is also supplying the tablet it will discharge faster than normal.
I’m not sure but I think that the model number may also be on the back cover, but I might be wrong about this.
Once you know the model number, search online using that information to find suppliers of the part e.g. Kindle (insert model number) digitizer (or touchscreen)