I never tried to this kind of stuff - my main goal was to get a convenient access to the Kindle so I can explore it.
I can make some guesses, though - make sure you have resolver configured (/etc/resolv.conf), also, check /opt/amazon/ebook/config/. From quick look firmware seems to be using http proxies, which may not make sense when you are accessing Internet through your ISP...
BTW, tcpdump or wireshark running on your host will tell you everything
