Flaming Armor can prevent damage that is being dealt by a Monster in combat or a Monster's ability. The source just has to be a Monster.
However...
The
Angel of Awesomeness is a special case. Her ability is moving two damage (tokens) from your Hero to a target Monster or Hero. This is neither
dealing damage to the target, nor is it
healing the Hero it comes from. It is just moving the tokens. (The card may be errata'd to specify tokens rather than damage to make this clearer).
So yes, Flaming Armor can prevent damage dealt by Monster abilities. It cannot, however, prevent the Angel of Awesomeness from moving two damage tokens to your card.