In John Updike's short story, "A & P," Queenie (as Sammy perceives her to be) comes into the grocery store where he works, with two friends, dressed in bathing suits. At the time this story was written (and even still in some places today), this was unsuitable attire in public locations like stores and restaurants, for example. This detail becomes the source of conflict between Sammy and his manager when his boss chastises the girls for their inappropriate attire.
To decide whether "Queenie" is a flat or round character, it is best to check the definition. Dr. L. Kip Wheeler's site on "Literary Terms and Definitions" defines these two terms:
E. M. Forster describes characters as "flat" (i.e., built around a single idea or quality and unchanging over the course of the narrative) or "round" (complex in temperament and motivation; drawn with subtlety; capable of growth and change during the course of the narrative)
Wheeler goes on to provide more specific detail:
A round character is depicted with such psychological depth and detail that he or she seems like a "real" person.
Also called a static character, a flat character is a simplified character who does not change or alter his or her personality over the course of a narrative, or one without extensive personality and characterization.
Studying these two definitions, it seems clear that Queenie's character is flat. She comes into the story and mesmerizes Sammy as she shops, but the reader does not know what she is thinking or whether she is as confident as Sammy perceives her to be. In fact, all of the information we get about Queenie comes through his adolescent viewpoint.
Poised on the edge of passage into the world of the adult—ready to leave childhood behind—Sammy thinks she is a goddess, but her character, in actuality, has no depth at all. Her presence is simply the catalyst for Sammy's change in how he perceives the world and his place in it.