I've had Kindles for years and never caught them "phoning home" without being told. I think it's okay.
But if you really are worried about it, I wouldn't bother with a lead cover--one of those foil bags that computer chips and circuit boards come in would do you fine and would be much lighter.
Anyway--couldn't you just not register it? Then Amazon might know there was a Kindle out there with such and such files on it, but wouldn't know who had it.
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