I loved the 8th gen sliding cover by sy69jl but I have a 6th gen Kindle, so I redimensioned it. See the spreadsheet for my calculations.

I also wanted an integrated book stand so I designed it.
It now works both as a screen cover and a book stand.

You will find a small piece of an overhang test model so you can test print whether you need to use supports. I didn't on my Anycubic Vyper.

You'll need to print two copies of the hinge socket.

A problem I needed to solve was that when the Kindle is faced up for reading, it fitted snugly. But when inserted face down it was a bit loose and could slip out easily. So I adapted the book stand to have a stop at the bottom edge. You will need to carefully place the hinged stand assembly so that the curved stop just clears the bottom edge when in its parked position.

I just used some glue to hold the hinge sockets in place, but the danger is that the hinge shaft might accidentally get glued in a fixed position and not work.
So I made 4 holes of 2.2 mm in each hinge. My idea is that for each hinge socket I would drill 4 holes in the case at the perfect spot for each socket, then thread some of the 1.75 mm filament, and use a hot soldering iron to the top to prevent it from moving.

Lastly, depending on which material you use, the hinged book stand may move TOO freely. So I allowed for a movement stop in each hinge. It's the slot in the middle that exposes the shaft. I thought to screw in an M2 self-tap screw at the point where I would want the hinge to stop rotating.
However, using PETG, the 0.5 mm clearance still allowed good friction and I didn't need to use that feature. Maybe if it loosens up I can implement it.

I used Tinkercad so you can remix it here:
https://www.tinkercad.com/things/fqmC4CaR5xH-kindle-6th-gen-sleeve
https://www.tinkercad.com/things/kJ7EQ10s5xY-hinged-book-stand-adapter