I would be shocked if a company of that size didn't patent a ton of things that involve their Kindle business -- paperwhite is a big selling point to them so if they didn't patent it originally, I'd expect that to have bought it or licensed it from whoever did.
Our operating company has 20 years of experience in creating and monetizing intellectual property in the US and abroad. I'd be glad to help.
This is a difficult question to answer, because consumer products as complex as the Kindle contain technologies / components that are in turn covered by many patents. Even when focusing on a specific element of its operation, there may be several patents that cover that element.
In general, think carefully about the process in question. In other words, how would you describe how Paperwhite technology works in terms that a layperson could understand? Then, break down that functionality into separate, elemental processes.
With that information, start searching (Google Patents is a good place to start) to see if there's any related intellectual property (IP). Make sure to look at directly related and even tangentially-related filings for hints, since large companies are good at creating IP that can obscure the true nature of processes / products that they cover.
Remember that in order to perform a thorough search, you will still probably need to enlist the services of an experienced patent attorney.
If you would like to discuss this in more detail, let me know - I've helped start-ups create IP strategies tailored to their specific products / services.