In "A Rose for Emily" by William Faulkner, why did the writer use a rose, not a flower, in the title of the story?

If I understand your question correctly, you're asking why the story is called "A Rose for Emily" rather than " A Flower for Emily," right?

First, let's take a look at Faulkner's own explanation for the title:

"[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." (This Faulkner quote comes from this book on Google Books.) 

Faulkner is saying that even though no one gives Emily a rose or even a flower in the story, he saw her as a women to whom one would want to give a rose, because they felt for her and her tragic situation. Many readers certainly feel that he accomplished this in the writing of the story, as even though Miss Emily is arrogant, haughty, and a creepy murderer, she is also a pitiable character. 

As to why Faulkner would use a "rose" in the title instead of another flower, or the word "flower" in general, I would say that the word was chosen for the connotations it evokes. A rose is a classic flower, just as Miss Emily is a classic example of an aristocrat from the antebellum South. Both are traditional and rather old-fashioned. Additionally, a rose is a traditional symbol of romance, and so it is relevant to the love story that Miss Emily was never really able to have.