Kefka was Amenheraft's eyes and ears, seeing what the king could not observe, hearing what the king could not perceive, and then letting the master of the nation know what was going on in the shadows, behind his back and out of the light.
He was a genius spy, able to form a complete picture of the situation from bits and pieces individual spies would feed him and had built an intricate web of relations all over the country and even abroad, using bribes, cohesion, blackmail, and even intimidation to get the information he wanted.
His intelligence web was massive and other than him, no one really knew the true extent of his reach or the total number of people under him.
For example, he was the mastermind behind the Agapios incident twenty years ago, where he was able to organize, infiltrate and smoothly exfiltrate one of the most secure houses in one of the most secure neighborhoods in the world of the time, which was in no way a small feat.