Characterization begins at the initial introduction of a character into a story, and the characterization of Miss Brill is no exception. From the beginning, Mansfield presents Miss Brill as a dynamic (changing), round (full range of emotions, reactions, motivations) character:

Miss Brill put up her hand and touched her fur. Dear little thing! It was nice to feel it again. She had taken it out of its box that afternoon, shaken out the moth powder, given it a good brush, and rubbed the life back into the dim little eyes.

She is presented as having emotional reactions; as having changes in motivations and behaviors; as having plans and ambitions. These all establish her as a dynamic and round character. Her range of emotion is shown in reaction to her fur: "Dear little thing! It was nice to feel it again." Her changes in motivations and behaviors are shown in the fact that she had done something before the story opens and now she is undoing it: "feel it again. She had taken it out of its box." That she has plans and ambitions is revealed in her treatment of the fur: "taken it out of its box that afternoon, shaken out the moth powder etc."

Having said this, we can jump to the end and analyze whether her characterization (1) has changed there (which would indicate a serious flaw in Mansfield's craft) and whether (2) Miss Brill is presented in that isolated spot as a round character.

First, the second to last (or penultimate) paragraph, clearly corroborates the analysis of Miss Brill's round, dynamic character presented in the opening lines. We clearly see motivations and that emotions and reactions change with changing circumstances, and we see plans and aspirations. Thus Miss Brill's characterization as a round, dynamic character is consistent throughout.

Second, what does an analysis of the last paragraph show? We see a number of changes in Miss Brill's emotions, behaviors, and motivations. We see that these are directly related to events that occurred at the park. We see that not only have the events changed her character for the present moment, but--based on the way she reacts to her "red eiderdown," her "fur" and the way she cares for the fur--we see strong indications that this unfortunate encounter with two rude and selfish people at the park may have changed her outlook on her life forever: she may have utterly reevaluated her inclusion in society and thus her happiness. This confirms Miss Brill as a round character.

She unclasped the necklet quickly; quickly, without looking, laid it inside. But when she put the lid on she thought she heard something crying.

If we are examining the distinction between "round" and "flat" characters based on the trajectory developed in the course of Mansfield's narrative, then I think one can say that Miss Brill is a round character.  She is fleshed out to the reader.  Detail is provided in which  the reader is able to fully identify Miss Brill both in the story and in their own lives.  She is developed.

I think that the distinction of characterization between round and flat has to go back to Forster's understanding of both.  For Forster, the "flat" character is one- dimensional and relatively straightforward.  The "round" character is more complex, one that is intricate, possessing alternate dimensions to their characterization.  Forster develops the idea that there is some level of change within the round character that is absent from the flat one. It is here where the ending of the story becomes essential.  Mansfield does not construct a "what will happen to Miss Brill" conclusion.  In refraining to do so, the reader must be able to figure this out for themselves.  It seems to me that if Miss Brill continues to engage in her Sunday routine without the awareness that she is merely a part in the production that she believes happens every Sunday, nothing changes.  The muffled sounds she hears from the fur stole go unheard and she is one- dimensional in the blame she heaps on it.  If she continues to engage in the routine, then she becomes flat in so far as that she has not changed.  She has refused to understand the nature of change.  If she decides to appropriate some of the experience from the narrative into life afterwards, then I think she becomes round in that she has changed.  The element of change is critical to Forster's "round vs. flat" distinction.  It is in this change where one has to examine the ending and determine for themselves if Miss Brill has demonstrated some change, something to the point where she is round or flat.