I don't think Burke will part with Kadri unless it's for Malkin or something. The guy not only has talent, he has the right attitude for the city and enough grit for a Burke team.
I don't even think he would trade him for Kovalchuk, considering his free-agent status. A Luke Schenn by himself, if he's still considered a top-5 type talent, is more than I think most other teams would give up for a rent a player. Hopefully, if this situation comes up, Burke can convince Waddell (and Burke is very convincing) that Schenn has top d-man potential.
Anyway, considering Atlanta is in the playoff race, and will almost definitely be in the playoff race come trade deadline, I really don't see them trading Kovalchuk.