Ah, but you do have a narrator: the narrator is the girl herself. Though many people have interpreted the story as a dialogue between a young girl and a very authoritarian maternal voice - I have always been of the opinion that it is an interior monologue. The girl is going through her day, doing her chores, and as she does so she is reciting the "do"s and "don't"s that she associates with each activity, all of which are, to a greater or lesser extent, designed to keep her in her place. Unfortunately, that place is in the traditional role of a traditional, subservient young woman of marriageable age.
What is interesting to me about the story is that she is beginning to question - perhaps as Kincaid herself might have - the contradictions implicit in each activity.
The girl can't really articulate them yet, but there is a sense that she is beginning to realize that is there something amiss in adhering to such rigid gender roles. It is almost as if she is beginning to turn off that internal censor that criticizes and condemns her every move.