USB and microUSB ports and devices that plug into them are designed to safely handle 4.75 to 5.25 volts, but many devices can operate on less voltage (even down to about 3 volts or so, and some have voltage regulators in them and can easily handle up to 12 volts).
The kindle can safely handle at least 5.25v on its microUSB port (and probably more), so at 5v you are fine.
There is a different problem. Kindles can occasionally require a full restart to free up memory and other resources when memory is getting full. Sometimes the kindle can automatically restart. Or it can just freeze up.
Try doing a restart from the settings menu when it acts strangely such as what you described.
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