Dee, at least in the story proper, is a static character: she doesn't change. Her goals are to take the Johnson family artifacts (quilt, butter churn) as museum pieces for which to brag about her rural Afro past. Her mother does not grant her either the heirlooms or even a voice. She is passed over and silenced, much like a stepsister in Cinderella.
As such, I think Dee is a flat character as well. First of all, this is a short story, and Dee only appears in half of it. Because her mother does not grant her wishes in the end, she does not develop enough, even though her name has been changed. Name alone does not a round character make.
Dee is also an archetypal Alazon, an impostor, one who thinks she is better and more deserving than she really is. She is driven by whim, fancy, and passion instead of substance, courage, and humility.
Round characters are usually challenged by something and it makes them change. Dee was challenged by poverty. She hated it from a young age so to get away from poverty and her childhood life, she attended school and changed.
Quite often round characters are a reader’s favorites but not so much in Dee's case as she is pretty demanding and has strong expectations. How ever she had changed through her education and social experience. She is in search of the roots of her culture and she changed her whims based on where she lives and her exposure to new attitudes about old things.