That doesn't quite work. It doesn't say "the anger of the Lord" incited David, it says He (the Lord) actually did;
Samuel 24:1 ...the anger of the Lord was kindled against Israel, and He incited David against them..."
Chronicles 21:1 "Then Satan stood up against Israel and provoked David..."
It's not identifying Satan with "the anger of the Lord", it's identifying Satan with the Lord Himself.
But God can still use Satan as a tool just as he has used many throughout history as long as you can agree that Satan can do nothing apart from the will of God. One possible example is God using Satan to tempt Job.