"Kindle" is an indicator led directly from the source voltage 1,2...1,5 V, so the voltage drop at the most LEDs not less than 1.6 V. And yet, if there is such a need, you can to make a simple circuit transistor blocking oscillator at the collector transistor which the inductance of the transformer will be inflated sufficiently high voltage to ignite almost any led.
The figure shows a diagram of a blocking oscillator operating since 0.8 V.
Transformer T1 is wound on a ferrite ring with a diameter of 7 mm (Cchhs). Winding twice folded wire sew 0,35, just 20 turns. After the completion of the winding beginning one wire to connect with the other end - this will be the withdrawal from the centre.
Mode you can configure the selection of R1.
Literature: