What literary devices does Jonathan Swift use in "A Modest Proposal"?

First, Swift employs dramatic irony: this is when the audience or reader knows something that a character does not.  Swift does not actually want anyone to eat babies; however, the speaker—a character or persona—does. The speaker thinks it's a great idea, but we are not supposed to agree (and hopefully we do not agree). We know this is a terrible idea while he does not, and so dramatic irony is created.

Further, the speaker says, "I grant this food will be somewhat dear, and therefore very proper for landlords, who, as they have already devoured most of the parents, seem to have the best title to the children." In this line, to call the food—babies—"somewhat dear," or sort of valuable, is an understatement; people generally think of their children as a great deal more important to them than only "somewhat dear." Moreover, he says that the landlords have "devoured" the parents, employing a metaphor. English landlords haven't physically ingested their Irish tenants, but they might as well have. The English seemed to get richer and fatter while the Irish got poorer and leaner. He implies that the English are consuming the Irish in such a manner that they might as well be physically eating them up.

Swift also uses paralipsis when the speaker says,

Many other advantages [of this proposal] might be enumerated. For instance, the addition of some thousand carcasses in our exportation of barrel'd beef: the propagation of swine's flesh, and improvement in the art of making good bacon, so much wanted among us by the great destruction of pigs, too frequent at our tables; which are no way comparable in taste or magnificence to a well grown, fat yearly child, which roasted whole will make a considerable figure at a Lord Mayor's feast, or any other publick entertainment. But this, and many others, I omit, being studious of brevity. [emphasis mine]

Paralipsis is when the speaker says they are not going to say something, and then they do say it. It generally makes the speaker look like they lack self-awareness and are, perhaps, a bit silly. They might ramble on and on, all while thinking that they are being brief and pithy. The speaker says at the end of the above paragraph that he "omit[s]" many of the advantages of his scheme, but he has just listed a great many and goes on to list quite a few more.