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.