Symbolism, Imagery, Allegory
White Flag
A white flag means to surrender, and when the Chairman gives Chiyo his white hanky, she surrenders her heart to him. She keeps it in her kimono, she rubs it for comfort, and she lies down and sniffs it to remind herself of her Chairman. It becomes an idol of sorts, and she worships it, because she thinks the Chairman is her savior.
Sayuri takes the hanky everywhere—to teahouses, on trips, and probably to the bathroom. It's her way of keeping the Chairman with her, even when she thinks that he is an impossible goal. We're not sure whatever happens to his hanky, though. After he chooses her, she never mentions it again. She doesn't need his scent, because she has the real thing.