In the real world one of the hats I wear is an information security officer and as such I spend my days worrying about just this sort of thing. What information on your kindle is secured information? Typically the credit card information and that's encrpyted. What does your kindle know about you? If it was a person you met on the street would it recognize you? no, does it know where you live? no, amazon's servers know that, it knows what you read, and I have freely told everyone on mobile read what I have read this year - its on my reading challenge list, go ahead take a look if you want. Your kindle does not know much about you, yourr mother and your wife knows a lot more about you then your kindle does.
My advice is stop worrying about this the kindle does not know much about you.