What?
They can use deadly force to stop a perp from fleeing. Even a citizen can in Tennessee. It might be hard to prove that you gave fair warning. But if you can, it's legal.
And I would think doubly so in the case of a 6'4" 292 pound perp who had already assaulted an officer. Because it's just too risky to go tackle him.
If Brown had his hands up surrendering, there would be no justification. But if Brown was fleeing the cop would be justified. If Brown was charging, the cop would be justified.