I’m not sure about functionality of the site, but the surfing capability of the Kindle is currently very limited.
In the shorter time frame, a simple e-book conversion button might be a good solution. Then the main study of words can still happen on the Lingq website while people would be able to read over and review the texts later on the Kindle (or whatever e-book reader). Longer-term I think this media holds great potential for your business model. I am personally waiting for more foreign language dictionaries to become available for the Kindle. This is surely only a matter of time.
Cheers
Rohan