You list the Jazz as one of your favorite teams, yet you don't want them to improve...interesting...
Anyway, I'm not sure about this trade. AK is very injury prone, but so is Carter. Both are having unimpressive seasons so far (Carter has only now redeemed himself and started playing some real ball). Vince excelles in offense and isn't a good defender; Kirilenko is an all-NBA defender who struggles with his shot. I think right now, defense is important for the Nets but offense if much more important. I agree with Voodoo Child, VC shouldn't be traded for someone who can't score more than 15 points in a game. Who'll pick up the scoring? With RJ injured, it's even worse. Gasol, on the other hand, is a great offensive player and he would improve the team if we trade for him.
So, we don't really need/want/should trade for Kirilenko right now, unless we trade RJ for him(I wouldn't be against that as long as Carter stays for a few more seasons and doesn't opt out, which can't be counted on), or a few benchies and picks (very unlikely).