After the "blink" resolves, the card I have on the battlefield now is no longer the source of the ability I have on the stack.
In the ruling it says that
112.7a. The source of an activated ability can perform an action even if it no longer exists.
So, the Avacyn source of the triggered ability no longer exists, but it should be flipped bottom-face up.
What will happen? Will a new object be created? Will the activated ability resolve without effect?