Flight mode exists because the FAA applies unsafe-until-proven-safe methodology to everything flight related (as they should). If flight mode mattered at all planes would be falling out of the sky on the regular, many people just leave their phones on the whole trip. The only reason I turn my phone off is because it wastes a lot of battery as it tries to manage tower hopping the whole time. Planes are getting blasted by RF in the cellular bands continuously from the ground, too, so this is taken into consideration in the design process.

Don't get me wrong the Kindle shouldn't do what it's doing but it's by no means a safety issue.