Specifically according to this article, after "October 30, 2008, the Federal Circuit handed down its long-awaited en banc decision in In re Bilski.", business method patent has to either (a) "transform an article from one state or thing to another" (which this patent does not) or (b) be "claimed as carried out with a “particular machine"", which apparently does not include a "general-purpose digital computer". And given that the patent does a piss-poor job of describing the kindle, I'm not seeing it.
The fact that this suit was filed months after this decision suggests that somebody thinks this is worth pursuing.
Of course, if I'm right about this line of argument, the whole 1-click thing isn't valid any more, either. Should be fun, right? Maybe this is where the trade is going to happen, especially since Apple is paying license fees to Amazon to use 1-click in the iTunes store.