Fitzgerald’s writing style fits the set up of his narrator revealing an old story to his readers that we get in the first paragraph. There is almost an old-fashioned feel about the prose: Mr. Button stands "upon the sidewalk, trembling from head to foot" (1.1.19); Benjamin is a baby of "threescore and ten" (1.1.39); when he gets married, the story of Benjamin’s birth is "sent out upon the winds of scandal in picaresque and incredible forms" (1.6.1). The narrator’s prose actually creates an old fashioned atmosphere.
You’ve also got the classic Fitzgerald imagism going on here. Although, in "The Curious Case of Benjamin Button" this imagery is less frequent than in, say, The Great Gatsby. Look at the passages where Benjamin falls in love, and notice the "eastern sky suddenly cracked with light" as "an oriole yawn[s] piercingly in the quickening trees" (1.5.24). You can see more examples at the end of the story, as Benjamin becomes a child playing with "little strips of coloured paper" (2.1.3) and finally remembers only "the warm sweet aroma of milk" (2.1.10). By using this sort of language, Fitzgerald hits all your senses as you read. Check out our discussion of "Tone," and think about the way this style works with the shifts in tone we find in "Benjamin Button."