I think your friend is wrong.
There were new rules in the US on some routes that banned laptops, tablets and even over-sized phones from cabin bags, but these are still permitted in checked-in bags.
https://www.switchedoninsurance.com/blog/flight-gadget-ban/
People did not want to put them in checked bags because they want to use them on the flight, and there is a risk of theft of high-value items from checked bags.
Spare lithium batteries (uninstalled) must be put in cabin bags and are not allowed in checked bags, but I've never heard of a ban or any other restrictions on Kindles etc in checked bags.
Having said that, a Kindle is so small and light that you might as well put it in your cabin bag, if you are in any doubt...
I routinely take a laptop, and a 99.96 Wh lithium battery in my cabin bags on flights all around the world. My Kindle occasionally comes with me, but always in the cabin bag, because I don't check bags in.
Good luck!