If the flickering is periodic (not random) it could be an aliasing effect from an undesired frequency getting into the circuit and "
ring modulating" the PWM (brightness) frequency giving the "beat frequency" flickering you describe. Also possible (but unlikely) that there could be some weird "relaxation oscillator" effect if there are some transistors in the circuit that are misbehaving. Or perhaps your kindle is possessed, and just needs a simple exorcism?
