What or who is the antagonist in “The Flowers” by Alice Walker?

Racism is the antagonist, the opposing force, in Alice Walker's "The Flowers." Myop begins the story as a carefree, cheerful young lady. Overall, she appears innocent and lighthearted as she goes for a walk by a nearby spring. Even so, we see a glimpse of the potential hurtfulness of humanity through the line,

She struck out at random at chickens she liked.

Though Myop is being playful, she's still scaring chickens who have not done anything wrong.
The story takes place in late summer / early fall. It's harvest season, and crops like corn and cotton are being reaped. She has the freedom in her schedule to be able to go for a walk and sing a song.
The story opens with a very positive mood. Diction such as "white bubbles" "gather nuts" and "bouncing this way and that" make the story seem cheerful and playful.
By the last four paragraphs, as she continues her walk, there is a distinct shift. The mood grows eerie and uncertain:

but the strangeness of the land made it not as pleasant as her usual haunts. It seemed gloomy in the little cove in which she found herself.

Then, when Myop steps on the decomposing body of a lynched man, the mood becomes dark:

His head lay beside him. . . Myop saw that he'd had large white teeth, all of them cracked or broken, long fingers, and very big bones.

Alice Walker concludes the story with the line,

And the summer was over.

On its surface, this line states that the season is shifting from summer into fall. It also likely signifies that Myop's season of innocence, her childhood, has come to an end. She sees evidence of a crime of hate. In this moment, Myop sees the workings of the antagonist, racism.

The antagonist in "The Flowers" is the violent, racist society in which Myop lives. It's this society and its warped values that are responsible for the brutal lynching of the man whose corpse Myop finds while playing in the woods one day. The story's set during the period of Reconstruction, when white supremacists in the South expressed their opposition to African Americans' newfound freedom and civil rights by acts of violence, murder, and intimidation. Lynching wasn't simply a means of meting out summary justice; it was a method of control, used by white society to keep African Americans in a state of permanent fear and subjection.
Myop's just a little girl; she's too young and innocent to understand any of this. But when she sees the man's corpse lying there in the woods, she instinctively knows that this is a place where something evil's happened. All of a sudden, her innocence has been shattered, and from now on her relationship to the society in which she lives is likely to become ever more antagonistic as she gets older.