"Opens then instantly quits" means "the app crashes immediately".
Back in the early days of Android the OS would tell you when an app "stopped unexpectedly", whereas iOS didn't - iOS users just found themselves back on their home screen. This led to many people assuming that Android suffered more app crashes than iOS, because iOS users often didn't realise what had happened (studies found that there were actually more iOS app crashes than Android back then, but the common perception was the other way round). Of course Google "fixed" this by removing the messages that told you the app had crashed. (This is a common approach to such problems. More than one phone manufacturer has "fixed" reception problems by changing how the signal bars are displayed without changing the actual signal reception at all...)
To be honest, there's probably not much you can do. You can report it to Amazon and hope you get a more helpful response than (a) being told that it's not compatible with your device or (b) no response at all, but I wouldn't hold my breath waiting for a fix. You could try installing an older version (apkpure have older versions of the Kindle app) and see whether that works. That's about all I can think of.