Odd that the kindle wifi mac is listed as PRIVATE??
Normally you can just look up the mac and get the maker, which can help you trouble shoot the issue.
Glad you figured out what it was by accident, but if you would of sniffed you would of seen it talking to where it talks to, etc And that should of pointed you to what device it was.
I have a cheapo netgear switch, and its "smart" and I can view mac addresses and such, just because its cheap does not mean it can not be loaded with features. I had picked up my GS108T for like $79, does vlans, mirror port, igmp snooping, lagg, qos, rate limiting, etc. etc.
Next time your in the market for a switch you might want to look for a smart one, normally only a few dollars more.