All the personages introduced into the narrative besides Miss Brill are flat characters. Specifically, there are only two other characters whose thoughts are revealed. They are the romantic couple who enter the narrative near the end. But, they do not change in their attitudes at all and remain flat.
Flat or static characters are simple characters; that is, they do not develop or change beyond the way that they are first presented; they remain the same throughout the narrative. In "Miss Brill," there is little characterization other than with the protagonist, Miss Brill herself. The only flat characters who enter the narrative for any length are the woman wearing the ermine toque and a gentleman in gray, whose brief interaction Miss Brill observes, and the boy and girl who sit down where an old couple has been on the bench on the opposite end of Miss Brill. When the boy attempts to be affectionate with his girlfriend, she protests, "No, not now....Not here, I can't." Her boyfriend protests,
"But why? Because of that stupid old thing at the end there? Why does she come here at all--who wants her? Why doesn't she keep her silly old mug at home?"
The girl laughs at Miss Brill's fur, then the boy tries again with her and she repeats, "No, not here..."
While their cruel words affect a change in Miss Brill, these characters remain the same, and are flat characters.