"Alyn was seeking for me, and I did not care to be found. He grows tiresome when he drinks, does Alyn. I saw you slip away from that bedchamber of horrors, and slipped out after you. I've had too much wine, I grant you, but not enough to face a naked Butterwell." He gave Dunk an enigmatic smile. "I dreamed of you, Ser Duncan. Before I even met you. When I saw you on the road, I knew your face at once. It was as if we were old friends."
Dunk had the strangest feeling then, as if he had lived this all before. I dreamed of you, he said. My dreams are not like yours, Ser Duncan. Mine are true. "You dreamed of me?" he said, in a voice made thick by wine. "What sort of dream?"
"Why," the Fiddler said, "I dreamed that you were all in white from head to heel, with a long pale cloak flowing from those broad shoulders. You were a White Sword, ser, a Sworn Brother of the Kingsguard, the greatest knight in all the Seven Kingdoms, and you lived for no other purpose but to guard and serve and please your king." He put a hand on Dunk's shoulder. "You have dreamed the same dream, I know you have."
As far as this go, Daemon Blackfyre is right: Duncan does indeed become a Kingsguard, and arguably the greatest knight in the land when he rises to the office of Lord Commander.