Question: Is it possible to get a refund from a publisher if I bought an article that contains a major flaw (i.e.,one that invalidates the main results or the main conclusions)? Assume the article was bought through one of the main academic publication's paywall.

Answer: 
Of course you can request one - just send an email. You'll brighten up the publisher's office for the afternoon, and they'll be chuckling all the way home.

So just as long as you don't seriously expect to get your money back, you'll be fine. When you paid your fee, you were paying for access to read the paper. As long as that access was provided, then the publisher has met their side of the bargain. Peer review is not a guarantee of correctness. It's a first-level junk filter, nothing more.

And on top of you getting what you've paid for, you've got the additional bonus that you've now got a new paper that you can write, that's practically already written itself; the paper where you take apart your bought paper's argument. Magnanimously, the publisher won't require you to pay extra for this bonus - you got it thrown in for free.
The publisher does not guarantee that the article has no major flaw. Indeed, for all they know, the reason why you requested access to the article in the first place was to refute it. Or to check other people's criticism of it.

Also, consider how many articles there are that are wrong yet of great historical interest. One example that pops into mind is the papers Einstein published before November 1915, containing his "work in progress" on general relativity, including some blatantly flawed thoughts.

So no, I do not believe you are entitled to a refund. You certainly don't have a legal basis, but I don't believe you have a moral basis either.

I can, however, imagine a scenario in which you might be legally entitled to a refund: if the article in question was based on fraudulent research, and the publisher was complicit in the fraud (e.g., the paper remains available for a fee even after it has been demonstrated unambiguously that it represents fraudulent research). Respectable publishers retract such papers. Other publishers... well, good luck with them.