Unexpectedly, counterintuitively and unfortunately, the Kindle does not charge via the Solio's USB socket adapter. The Kindle seems to be extremely selective in what DC input specifications it accepts, either intentionally or not. Only the AC to USB adapter the Kindle ships with and "most" computers' USB ports seem to work. I've tried it with several adapter configurations with no luck (some battery-based, some AC-based, etc.). To further confirm this problem, an Amazon tech support rep I spoke with about this mentioned it's not working on some computer brands' "front external" USB ports, either. Presumably due to voltage drops, etc. He said it was becoming a major headache for them. He said sometimes you have to try plugging it into several different USB ports on the same computer until you "find one that works." Seems like a definite design flaw in the Kindle 2. To not be able to charge it, straightforwardly, with a portable USB charger is a pretty unfortunate and unnecessary limitation for such a portable-oriented product.
There's a car/auto/cigarette lighter adapter that Amazon sells called the "Rapid Car" that I hope will work, albeit in a somewhat Rube-Goldberg-esk way.
Amazon claims/confirms it's "designed to work with the Kindle 2 and DX." I just ordered one and will post the results once it arrives. In theory you should then be able to use it with the Solio's cigarette lighter socket adapter. There are also small emergency-oriented devices that take AA batteries and sport a cigarette lighter socket for an output, that would then also work.
Oddly, the same company (Gomadic Corp.) that makes this adapter, also makes a battery pack that supposedly charges the Kindle 2. However, two of the three product reviewers on Amazon claim it didn't work for them. Not a vote of confidence for Gomadic's Kindle accessories, but we'll see, there seems to be several reviews claiming the Rapid Car worked and charged the Kindle 2 (albeit, no doubt, from a heavy-amped car socket and not a little Solio attempting to match it's mystery device's load/amp requirement via it's electrical sniffing process).
Perhaps we'll have a workaround via this Rapid Car, or perhaps other 3rd party products, but it appears some Amazon engineers dropped the ball on this whole "USB charging" thing. The devil is always in the details, no?