I've worked quite a bit with solar chargers for Kindles. The main Kindle models I've powered are Kindle 4/5's and Kindle Keyboards (3rd edition). Let me try to answer your specific questions first, then I'll go into more background in case it's useful to you and others:
e-ink Kindles need somewhere between 500mA and 700mA to charge effectively @ 5v DC. They have a battery of roughly 2000mAh depending on the model, so charging can take several hours. Most integrated solar chargers include some or all of:
a solar panel :) These range from milli-watts fitted to the battery case, to several watts where the battery is often separate from the panel (but may be stored at the back of the panel).
voltage regulators and convertors between the panel and the battery and the battery and the device it's charging
- a Li-Ion battery, similar to those fitted to mobile phones. Some with larger capacities include several batteries.
There are various options available, depending on your budget and what you need.
Solarmio provide integrated covers with an inbuilt solar panel on the front and light inside the cover. These are available for the Touch and the Kindle 4 http://www.solarmio.com/en/4712389290168.aspx (for the Kindle 4 model). I have 2 of these currently and they seem to work very well with no complaints from the end-users (schools in Kenya). Similarly, http://www.worldreader.org have used lots of these cases and they are reliable in use.
I also use 3 watt panels which I connect to a generic USB battery-backed recharger. The battery stores the charge from the solar panel. From my testing of using 3 watt panels to charge Kindles directly (without an intermediate battery) caused the Kindles to hang and need rebooting, the charging didn't deliver consistent voltage (5v DC needed by the Kindle). For more info here's a blog post I wrote about some of the challenges http://kusaidiamwalimu.org/musings-on-solar-power-and-usb-batteries/
Picking suitable panels and batteries can be a challenge to find ones that are reliable yet cost-effective:
- Many integrated small battery-based units with small built-in solar panels don't generate enough charge to be usable (I've tested them in various countries including Kenya near the equator in peak sunshine).
- Similarly, most of the models I've bought have failed with the Lithium-Ion batteries swelling sufficiently to explode the case. These tend to be delivered from China or Hong-Kong, via eBay. I deliberately bought various no-name units to test their viability for my e-reader projects where I provide Kindles to schools in Kenya, etc.
The 2 models of batteries I've found useful include a 5000mAh unit, I pay around £10 per unit on eBay.co.uk, and small 1800mAh batteries from Volt http://getvolt.dk/en/ (they don't currently sell them to end users, I happened to meet one of the founders and eventually obtained several to support my e-reader projects in Kenya). Here's a recent blog post about using the Volt batteries in Kenya http://kusaidiamwalimu.org/solar-powered-kindles-with-e-volt-batteries-at-nyabondo-school-oyugis-kenya/
I'd love to learn more about how other people fare with solar charging of their e-ink devices. FYI: I'm also going to be creating larger solar charging systems to charge tablet-based ereaders and devices e.g. such as Nexus 7 and iPads.