I'm on Windows 10 using Kindle for PC v1.24.51068
My observations are that it is fairly easy to avoid the unwanted upgrade but it will be tedious if you open it many times per day.
When the Kindle app is opened it starts to download this file - whether you want it or not:
Code:
C:\Users\<myusername>\AppData\Local\Amazon\Kindle\updates\KindleForPC-installer.exe
When you close the app it runs this downloaded installer
[ETA: or maybe it runs it when you next open the app]. So you can avoid the update running by deleting this file before you exit.
It should work for now but I wouldn't expect this workaround to be anything more than a sticking plaster until Amazon find a more sophisticated way to force their upgrades and KFX format on you.