What are some rhetorical devices in "A Modest Proposal"?

Rhetorical devices are persuasive devices. To understand the rhetorical devices Swift is using, it is therefore helpful to understand what Swift is trying to persuade his readers to do.
As a high ranking clergyman in Ireland, Swift was concerned with the plight of the poor and increasingly frustrated that year after year reasonable, mild, and doable solutions to the problem of acute poverty were brushed aside by the people with the power to make changes. Swift wanted to see starving mothers and children fed, tax burdens on the poor decreased, rents lowered, and decent job opportunities created. However, perceiving that sensible, rationale arguments were going nowhere, Swift determined to try a new approach.
Central to this approach is hyperbole or exaggeration. Swift hoped that by creating a morally clueless narrator with a completely outrageous solution for the problem of poverty in Ireland, he would shock people and gain their attention. Ultimately, he hoped that the essay would encourage people to see and adopt some of the moderate and humane ideas for alleviating suffering that he slips into the narrative.
The main instance of hyperbole Swift lights on is the idea, stated with tongue-in-cheek or ironic seriousness, of encouraging parents of the poor to fatten up their infants and sell them at a year old as a dinner delicacy to be served at the tables of the wealthy. Swift buttresses his hyperbole with graphic imagery, such as the vision of a plump baby served steaming at the end of a knife, and a "logic" that entirely misses the point that human lives are in question, not simply pins or some item made to turn a profit.
Swift's strategy worked to the extent that people paid attention and were deeply shocked by his narrator's suggestion, but rather than lead to positive reforms, it lead instead to Swift being castigated as a warped misanthropist, because people mistook the essay's narrator for Swift himself. Early readers missed the irony and hyperbole and took Swift as making a serious suggestion that they found repugnant.

"A Modest Proposal" is a Juvenalian satirical essay whose title drips with irony. The proposal the author makes is anything but "modest." Since the British have had such a heartless attitude toward the Irish in general, Swift employs biting irony and hyperbole to suggest that the rich British gentlemen and ladies may just as well eat the poor Irish children: figuratively speaking, they have already been "eating" Ireland.
In another example of irony, Swift adopts the tone of a financial adviser while discussing the "breeders," how many children will be produced, the season in which many Irish Catholic children are born, and the reduction of "papists" that will occur if the "proposal" is accepted. Moreover, he has calculated the profit for the landlord if the Irish baby is made into "four dishes." With a polite and deferential tone for such a barbaric message, the satirical effect is enhanced. 
Later in the essay, Swift makes a logical appeal (logos) that is also ironic. He writes,

Some persons of a desponding spirit are in great concern about that vast number of poor people, who are aged, diseased, or maimed,. . . but I am not in the least pain upon that matter, because it is very well known, that they are every day dying, and rotting, by cold, and famine, and filth, and vermin, as fast as can be reasonably expected. 

The use of the word reasonably suggests a logical appeal, but it is ironic because it assumes that the readers of the essay reasonably expect the poor class to die by hideous means. This appeal should evoke an emotional response of horror. Further, Swift's speaker makes other logical appeals by using statistics on appalling topics. Finally, he concludes with an ethical appeal to demonstrate that he is fair, trustworthy, and devoid of an ulterior motive. This conclusion is ironic, also.
https://www.britannica.com/art/Juvenalian-satire

The speaker uses logos, or appeals to his readers' logic, in his arguments for eating babies. He offers his calculations that of 120,000 children, it would be appropriate to reserve 20,000 "for breed," a quarter of which should be male (just as is done with livestock, which makes it all the more logical to him). Then he reasons that a "plump" child will "make two dishes at an entertainment for friends," and if one's family dines alone, there will be leftovers for lunch the next day. All of these calculations are meant to convince us to understand the supposed logic and reasonableness of this proposal. The speaker employs logos again when he discusses the other benefit of his plan: that it will lessen "the number of Papists among [them]." He tries to appeal to readers' logic in order to convince them of his point.
The narrator uses litotes, when one denies the opposite of the thing one means, when he says that "butchers we may be assured will not be wanting." He means that butchers will have lots of new business as a result of this new meat source, but he has suggested this by saying that they will not want for business. He employs litotes again when he says that, if certain young women who are of no benefit to the community had been disposed of in a similar way, "the kingdom would not be the worse." He means, of course, that the kingdom would be much better off without them.