What are some examples of figurative language in chapter 13 of To Kill A Mockingbird? Why are they significant and how do they add to the craft of the novel?

Much of the figurative language in Chapter 13 revolves around describing Aunt Alexandra, who has come to stay with the Finches. It shows how she fits perfectly into the white social world of Maycomb yet is very different from Atticus, Jem, and Scout.
Lee uses irony when she writes that Aunt Alexandra:

did not permit Calpurnia to make the delicacies required to sustain the Society through long reports on Rice Christians

The irony underscores the cluelessness and perhaps hypocrisy of the typical Maycomb ladies: many readers of the novel would consider it in poor taste for the ladies to be eating "delicacies" while discussing "Rice Christians," a figure of speech describing people in other parts of the world who converted to Christianity because so they could be fed. Yet the Maycomb ladies are oblivious to what they are doing in eating well while discussing the starving.
Lee also uses a figure of speech in using the term "royal prerogative" to describe Aunt Alexandra:

given the slightest chance she would exercise her royal prerogative: she would arrange, advise, caution, and warn.

Of course, Aunt Alexandra is not royalty, but the term helps convey how imperious she is, and how, like royalty, she never questions her own view of a situation.
Scout describes Maycomb as "an island in a patchwork sea of cottonfields and timberland." This is figurative in that Maycomb is not literally an island. Further "patchwork" conveys the image of a quilt: the fields and woods are not a quilt, but they create a pattern that looks like a quilt. Scout wants to convey that Maycomb is a world unto itself within that pattern. The important point, however, is that Aunt Alexandra ideally suited to the "island" of Maycomb. We learn from Scout that:

Aunt Alexandra fitted into the world of Maycomb like a hand into a glove, but never into the world of Jem and me.

"Hand into a glove" is another figure of speech, one so overused we might call it a cliche. But using a cliche is a good way to communicate the way Aunt Alexandra melds with the unreflective, very conventional Maycomb society.
Lee also uses figurative language to describe the differences between Atticus, Jem, and Scout on one hand, and Aunt Alexandra on the other. Scout wonders if her aunt is a "changeling" or born of "mandrake roots." Both are mythic allusions that suggest that Alexandra actually is not a blood relation to the rest of them. But what Scout really means is that it is stunning how different they are.
When Jem mentions all the disreputable stories about their cousin Joshua, we learn that

Aunt Alexandra was standing stiff as a stork.

Stiff as stork is a simile that emphasizes how disapproving Aunt Alexandra is of hearing anything other than heroic or flattering cliches about their ancestors.
The figures of speech function and add to the craft of the novel by emphasizing how different Aunt Alexandra and most white Maycomb people are from Atticus, Jem, and Scout.