In what sense does the narrator's telling of "A Rose for Emily" serve as a metaphorical rose for Emily?

This is a great question to ponder, especially since actual roses never appear in the story.

The last section of the story, Part 5, gives us our only hints of literal roses. As the townspeople break into Emily's bedroom upstairs, they see how everything in the room has a paleness to it, even the "faded rose color" of the curtains and the "rose-shaded lights." Roses are a symbol of romantic love. Since we only saw these rose-colored things in the very private bedroom belonging to Emily, we could infer that romance was something close to her heart, something only she really knew about.

The story is like a rose for Emily because the narrator wants to show his respect for her and bring some beauty and dignity to the story of her life. Giving a rose to someone also expresses romantic love; Emily deserved that and never got it.

We know that Emily was upright and proud, even irrationally so. But she also endured hardships, like her father's death when she was young, and the fact that while he was alive, her father chased away all the young men who would have been interested in her. That's more than just sad or annoying: having a husband would have given Emily the chance to earn respect and find fulfillment as a wife and mother, and it would have allowed her family line to continue. But as it actually happened, her entire direct family line was wiped out because of her failure to marry or have kids.

As it turns out, a bit of Googling reveals a quote from an interview with Faulkner, the author, who explains his intended meaning in slightly different words. So let's check that out:

"[The title] was an allegorical title; the meaning was, here was a woman who had had a tragedy, an irrevocable tragedy and nothing could be done about it, and I pitied her and this was a salute…to a woman you would hand a rose."

What he means is that the storyteller feels pity for Emily's situation and wanted to "salute" her, or respectfully acknowledge what she had endured.

Still, you don't have to limit your thinking to what Faulkner himself says. Stories take on lives and meanings of their own, and you could continue to think about what else a rose might symbolize and how that might deepen your understanding and appreciation of the story.