Okay, this is the best one yet and it’s super light and simple.
I took some 9 gauge aluminum armature wire that I had lying around (you can buy much more of this than you need for this via Dick Blick), I then stuck one end of it in the headphone jack on top of the Kindle, bent and shaped it into an arm, then added one of the new Maxell CR2032 Micro Lithium 3V batteries that I received today ($3 per), and taped the battery to the armature wire and then simply slid two LEDs ($1 each) onto the battery and voila! This gives a nice full Kindle light dispersion.
For the next version: I will move the battery to the back, add a switch, run wires up the armature to the two LEDs, and probably wrap the armature in electrical tape and add some sort of dome to keep the lights from shining in my eyes.
UPDATE: Slightly improved version of prototype C with arm going behind instead of in front and 3 LEDs here: