That's a really good question. I thought the answer would be obvious, but I can't find ANY information online about the legality of animals purchasing plane tickets. I'm sure stuff like that must come up - as, for example, all those cases where cats get left millions of dollars by batshit old lunatics; surely, "the cat", or at least someone connected with the cat's estate, would wind up buying plane tickets at some point? - but I dunno. I really don't know.
That said, YES. A pig CAN fly - if he is an emotional support animal, accompanying a human.
Here is an article on that. I don't know if Helper Piggies are still allowed on civilian aircraft post-pandemic, but as of 2019 there were documented cases of pigs flying.
There are also documented cases of
livestock pigs being airlifted around the globe, and according to Fox News,
shipping pigs via aircraft is a growing industry.
However, as for whether or not pigs can
freely and consensually purchase their own airplane tickets - I can't say. I'd like to say that, in the absence of any laws
against it, then yes they could. But I think this is a question that we'd need to send to a lawyer, maybe even a dedicated airplane lawyer.