The "horror" in any Shirley Jackson tale is less rooted in the standard sources of narrative horror (death or some other violation of the body's intactness) than in social fears. Regardless of what else takes place in a work of hers—or how successful the work is overall—Jackson is always most effective at conveying moments of social discomfort and disorientation. Even her most famous story, "The Lottery," is best seen, I think, as largely about the moment when a social insider suddenly finds herself on the outside. To anyone on the inside of a social construct or hierarchy (who has seen that structure as ultimately protective), the most existentially disturbing event would be when one sees the structure turn toward one as a foe.
"Flower Garden" takes its time in establishing the parameters of its conflict. The first half of the story is marvelously misleading. The younger Mrs. Winning, daughter-in-law of the elder Mrs. Winning, lives a narrowly circumscribed housewife's life, rigid in its regularity. For reasons not fully spelled out, but probably due to her husband's laziness, mentioned much later in the story by a secondary character, Mrs. Winning's expectations for a more aesthetically beautiful and satisfying life have been thwarted. Jackson presents us with a woman who is resentful but who has mastered ways to leave her resentments unaddressed or concealed. When a new neighbor finally moves into a nearby house Mrs. Winning has long wanted to live in (and about which she has meticulously fantasized painting and decorating), our protagonist largely suppresses her envy, taking pleasure in how well the neighbor's vision for the house matches her own. Of especial interest is the nascent garden. The Winning grounds don't get enough sun for a decent garden, but the modest cottage has enormous potential for beautiful gardens, and the new neighbor has brought a grand vision.
Though Mrs. Winning and her mother-in-law are both married, we only glimpse the spouses (and at first it seems they're both widows). The new neighbor, Mrs. MacLane, is actually a widow, and both women have six-year-old sons. (Mrs. Winning also has a baby of unidentified gender.) Though it appears that Mrs. Winning and Mrs. MacLane may not bond, in time they form a friendship built around daily market walks (clearly inspired by Jackson's actual walks in Bennington, Vermont, which also included a difficult hill), watching their children play, and having tea together.
Then comes an awkward encounter with a young black boy, Billy. Mrs. Winning's son uses the n-word—and Mrs. MacLane's son repeats it. Mrs. MacLane is ashamed and confused, whereas Mrs. Winning's focus is on her friend's reaction and the unfamiliar tone in her friend's voice as she reproves her son. To Mrs. Winning's dismay, Mrs. MacLane offers Billy a job helping tend her gardens; the next day, the boy's father shows up, and their agreement that this man—a widower whose wife was white—will work on the gardens finally establishes the story's crisis-bearing conflict for the third act.
There's no great drama to the tale in the end, and there's no revelation by our protagonist. But like "The Lottery," the story establishes both that there is a way the world is supposed to run and that the pressures to maintain that status quo are enormous even if unstated and unstatable. No one in the story ever addresses the source of the town's discomfort in the relationship between Mrs. MacLane and her hired man. Disapproval and social withdrawal are employed rather than anyone naming the source of the conflict.
In the end, Mrs. MacLane, who has moved from "the city" and may need to move back, is baffled by the people around her. Nothing truly horrifying happens, unless it is Mrs. MacLane's recognition that the ways of some people can never be changed.