Hmm. I think you're probably okay, actually; I just went looking, and it seems that despite it being an Android device, Amazon was determined to keep it separate from Google, so there are no Google location-enabled apps:
Don't log in to Google on your Kindle browser so it can't track you ther, and you should be all set; it's safe enough to check you mail from the mail app. The most Google will be able to tell is that you're checking your mail from your Kindle (it will probably pick up basic device identifiers, but nothing that will tie directly to you).
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http://m.xconomy.com/3376/show/ac0346373fadfa337cb195a7045c5a30/
Don't log in to Google on your Kindle browser so it can't track you ther, and you should be all set; it's safe enough to check you mail from the mail app. The most Google will be able to tell is that you're checking your mail from your Kindle (it will probably pick up basic device identifiers, but nothing that will tie directly to you).