As he is presented in the story, Bailey is most certainly a flat character. He is uncomplicated and he does not undergo any significant change in the story.
Because the grandmother is set in her ways, readers might be inclined to conclude that she is uncomplicated and one-dimensional. But she is in fact a round character. She is more complex than her nagging behavior lets on. She portrays herself as a good Christian woman, but she shows a racist side. She has good and bad intentions. She seems to nag her son and his family, but in her defense, she is poorly mistreated by her grandchildren. O'Connor points this out quite bluntly after the car accident:
“But nobody’s killed,” June Star said with disappointment as the grandmother limped out of the car, her hat still pinned to her head but the broken front brim standing up at a jaunty angle and the violet spray hanging off the side.
June says this with "disappointment." The grandmother brings the cat that causes the accident, but she couldn't have foreseen this. She proclaims the Misfit's name when she recognizes him. This also puts them in a worse situation, but she could not have foreseen this either. She is presented in a largely unflattering way in the story and this is intentional. The reader will consider if she is a "good" woman. The very notion suggests a "flat" type of character: one only capable of goodness and is therefore uncomplicated, unchanging: flat. But the grandmother is not wholly good nor is she wholly bad. She is good and bad. And she shows the ability to change at the end of the story. Whether that change is a selfish strategy for survival or a legitimate religious awakening, she does show that change.