External USB storage of any kind shouldn't cause BSOD.
First make sure every kind of Autorun and Autoplay is disabled. No-one ever needs autorun on anything. It's possible some legitimate file is on the Kindle and not on a flash drive that is autorunning or autoplaying. The only more stupid thing is upnp.
If still an issue:
I'd go to device manager, remove/delete any USB devices and let the OS re-install. A reboot may be needed.
Also make sure no AV or storage monitoring is running.
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