Can I activate abilities in response to spells?
Yes.  You can activate an ability (unless restricted) any time you have priority. Once the spell is on the stack, you place the ability of Caldera Kavu on top. That resolves first, so Kavu is black. Then Kill! Destroy! rechecks the targeting. Since it is invalid, it fizzles and is countered. 


  112.3b Activated abilities have a cost and an effect. They are written as “[Cost]: [Effect.] [Activation instructions (if any).]” A player may activate such an ability whenever he or she has priority.