What literary device is this quote? "Every one suspects himself of at least one of the cardinal virtues, and this is mine: I am one of the few honest people that I have ever known."

This sentence in The Great Gatsby comes at the end of chapter 3. Nick Carraway, the narrator, says this about himself. The primary literary device in this quote is irony. Nick has already informed the reader of numerous instances when he did not speak or act with complete candor. By telling the reader that he "suspects" he is honest, and having already established this is probably not the case, Nick compels the reader to examine his entire narrative for untruths. In addition, by isolating honesty from the other virtues, Nick encourages us to think he does not possess any of them, either.
Another literary device used is hyperbole, or extreme exaggeration. Nick compares himself to others as one of the "few" honest people he knows. Almost certainly, he knows more than a few. Nick is exaggerating to place himself into a narrow stratum. This exaggeration strengthens the irony, as his statement is not likely to be true.
In the first few pages of chapter 1, Nick made the point of sharing a few aspects of his personality and the problems it has caused him. He is the type of person that others find sympathetic. He constantly finds himself listening to other people's problems. He says that "curious"—meaning peculiar—people and "the abnormal mind" always figure out that he is a good listener. The dishonesty that Nick mentions at that point is not lying but faking various attitudes so that these people will leave him alone:

Most of the confidences were unsought—frequently I have feigned sleep, preoccupation, or a hostile levity . . .

Nick has come East in part because people in his hometown were starting to believe he was engaged to a young woman. Daisy raises this claim in chapter 1:

We heard you were engaged to a girl out West.

To them, Nick dismisses this as "libel"; to the reader, he states that he "had no intention of being rumored into marriage." Nowhere does he say what he told the young woman when he left; this method of removing himself from this "libel" can be considered dishonest.
At the end of chapter 3, just before he writes of himself as honest, he has been driving with Jordan Baker from New York City, where they were partying with Tom and his mistress. Nick is definitely interested in Jordan, but he admits to himself that pursuing an involvement with her would be unethical. He intends to behave as the honest person he wishes he had been all along:

. . . there was a vague understanding that had to be tactfully broken off before I was free.