I'm pretty confident that any device that satisfies a need, offers convenience, and is priced correctly, is likely to do well and to "catch on". I'm also pretty confident that the Kindle, or eBook readers in general since the Kindle isn't released globally yet, will become quite popular for school kids and college students in the years to come, since they will eliminate the need to carry heavy text books all day. I don't think the Kindle is quite there yet, however, even with the DX. Scribbling notes with a pen is still far easier and faster to do than using the Kindle's keyboard to make notes. But it's something to aim for, and probably not too far away.
As for more kids simply reading for enjoyment on a Kindle, I think that will be a direct consequence of using eBook readers in schools. I don't think we'll see an adoption rate anywhere near as large as the iPod, since paper books aren't going away and I'd guess there's a higher population of kids who listen to music than read, but I'm certain the Kindle and other eBook readers will become more popular over the coming years, as more people become aware of their existence.
For everywhere outside the US where the Kindle isn't available, eBook readers are a mess, and until formats are standardised, DRM is sorted out, and more places sell content for them, kids (or anyone for that matter) definitely aren't gonna be choosing them over good old-fashioned reliable paper books.