(And, yes, unless apocalypse, and unless battery dies, I know.)

Simple batteries can be made from readily available materials post apocalypse such as potatoes or citrus fruits like lemons. You'd need a fair amount of them for any appreciable time. After the fall of civilization, such required foods would be considered offerings to the gods to grant the knowledge stored on your Kindle long after its Lithium battery bit the dust. This would be until humans are able to make lead acid gravity cells, which again, isn't that difficult. They aren't very portable, but if you are just needing to run the device you don't need it to be.