Good morning Robert,
When you say allow, do you mean allow them to be used for School owned/managed content? Or just allowed in the attach to the network sense?
We don't actively restrict Kindle use, but we also only distribute e-books via Sora, which requires a whole sharing process to read on a kindle. I don't see a lot of Kindle products in the building generally.
Network wise, those things use so little data as to be inconsequential. Having extra devices using space on your ARP tables may be of concern if you're talking about 500 kindles, but otherwise, shouldn't pose a real problem for your network. Just keep personal devices separated from school devices and you're set.