Is it permissible to take the two sheep from one's father to distribute them in fulfillment of a vow, and then pay their price after receiving one's salary? And is there anything upon the questioner for doing so?

The Almighty says: "And let them fulfill their vows." The Prophet commanded the fulfillment of vows of obedience. If you have done the vowed act, you have done well, and there is no harm in taking it from your father's sheep, and you should thank Allah for that.