Well, this is my sort of field (I'm an EE, I do stuff like this for a living).
You can make/create a solar charger but the problem is that you'll need a battery + regulator in the 'assembly' to ensure that the USB connection gets a steady 5V @ 500mA or more if needed - at least if you want to do it 'right'.
What'll happen if you don't have a battery to buffer the panel is that the lipo controller chip in the Kindle will be switching on/off intermittently and that could have a knock-on effect to the K3 as it keeps changing its status.
Yep, sure you can try it the hack way and likely it'll work okay for a while - but I guess I'm talking from the other side of the fence where you can't afford to have things 'go wrong' lest consumers rip your soul out
Paul.