Ever read a boring textbook and realized halfway through that you didn't understand a thing? Yep, that's about the writing style Swift is aiming for. He packs so many big words and numbers into a sentence that it's hard to tell when he's being serious. Try this sentence on for size:
I think it is agreed by all parties that this prodigious number of children in the arms, or on the backs, or at the heels of their mothers, and frequently of their fathers, is, in the present deplorable state of the kingdom, a very great additional grievance; and therefore, whoever could find out a fair, cheap, and easy method of making these children sounds useful members of the commonwealth would deserve so well of the public as to have his statue set up for a preserver of the nation. (2)
Whew. Try saying that all in one breath. Swift likes his sentences on the lengthy side—that's how you know he's a politician. He's also satirizing political pamphlets in the style of ones he's already written, like Drapier's Letters.
Okay, so Swift might be making fun of himself a little bit. He knows that many of his readers are expecting A Modest Proposal to be a tad on the pretentious side, so he plays into that expectation with paragraph-long sentences and five dollar words. That's why it might take a while to figure out that he's joking.