Here's a quote from Encarta:
Despite jade's close association with China and Japan, its name has no Asian connections. It is of Latin origin, and started life as a description of the stone's medical applications. Latin ilia denoted the "sides of the lower torso," the "flanks," the part of the body where the kidneys are situated. A derivative of it passed eventually into Spanish as ijada . It was thought in former times that jade could cure pain in the renal area, so the Spanish called it piedra de ijada , literally "stone of the flanks." In due course this was reduced to simply ijada . French took it over as ejade , but subsequently l'ejade "the jade" became le jade , from which English jade is derived. ( Jade's alternative name, nephrite, is based on the same idea: it comes from Greek nephros "kidney"). For the nag one, it said 14th century, origin unknown.

I also looked up flank and, out of curiosity, nag. Encarta for flank:
[Pre-12th century. From French flanc , of uncertain origin: probably from assumed Old Frankish hlanca "side," from a prehistoric Germanic base that is also the ancestor of English flinch.]

M-W on nag:
Main Entry: 1nag
Pronunciation: 'nag
Function: noun
Etymology: Middle English nagge; akin to Dutch negge small horse
Date: 15th century: HORSE; especially : one that is old or in poor condition

Main Entry: 2nag
Function: verb
Inflected Form(s): nagged; nag·ging
Etymology: probably of Scandinavian origin; akin to Old Norse gnaga to gnaw; akin to Old English gnagan to gnaw
Date: circa 1828
intransitive senses
1 : to find fault incessantly : COMPLAIN
2 : to be a persistent source of annoyance or distraction
transitive senses
1 : to irritate by constant scolding or urging
2 : BADGER, WORRY

That's pretty cool to learn, that Dutch negge (small horse) and Norse gnaga (to gnaw) led to the same modern-English word. (Though I know this is old news to some.)

Wow--wow! I just noticed...l'ejade "the jade" became le jade . That's like, that's like, in English, a nother became another, don't you reckon? And you know what else? I can't think of anybody here in town that I could tell that to, that wouldn't just pat me kindly and turn away, but HERE, I can. Thank you, thank you!

Now, Aunt mav--see what you made me do?? Learn something!
Thanks! You know what else would be cool? If your jade word had opposing meanings, like cleave. (What's the word for that?)