There are a few reasons that Z.Z. Packer could have called the short story "Brownies". The most obvious reason is that the main characters, including the narrator Laurel, are part of a Brownie troop, called troop 909, who are on a camping trip at Camp Crescendo.
However, the title could also refer to the racial elements of the story. The girls from troop 909 are all African-American girls who have never interacted with white people, until they meet the other troop at the camp that consists entirely of white girls. So in this respect, the word brownie could refer to a more neutral color that could potentially bring the two troops together. That they don't come together could be to the attributed to the fact that the story, perhaps purposely, does not represent people considered to have brown skin. Instead, it is one extreme against the other.
In these terms, the reader could see brown as the color, much like grey, that could potentially provide balance and fair thinking. In the story, for example, the black girls, in their hatred and no doubt fear of the white girls, decide to beat up the white girls because someone thinks they overhead one of them use a racial slur against them. While they may have said the word, it turns out the white girls have learning disabilities and the habit of repeating words without understanding there meaning.
So while they must have heard the word from somewhere, and while that confirms that society is racist, it also suggests that there is potentially neutral ground such as the Brownies, where race shouldn't matter.