Killer instinct is about being aggressive and finishing your opponent without hesitation.
I wouldn't say getting angry is the right way to go. Sure, getting angry will give you a sort of "killer instinct", but you'll also get sloppy. You'll throw your technique right out the window, your breathing will go to shit and you'll expose yourself to counter strikes.
Killer instinct is also more than just being able to attack when you see an opportunity. There's a fine line that you have to cross between the two. There's a difference between thinking, "When I see an opening, I'll attack", and, "When I see an opening, I'm gonna do everything in my power to hurt him and finish this fight."
The difference is all in your mindset. Before you fight, you have to be 100% prepared to do what you have to do. If there's any doubt in your mind about hitting and hurting someone, then you'll have a split second hesitation before you strike. You need to commit your mind and body 100% to attacking and hurting someone, that's what fighting is.
You can't be afraid to hit, and you can't be afraid to hurt someone else.
I think the anger part comes in because, like some other guys mentioned, a lot of fighter's have gone through tough shit in their lives. Because of the things they've gone through, they've already reached the point where they have no problems taking hits and hurting their opponent.