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.
There's only a few narrow reasons you might demand a refund in this case: first, if the download/manuscript was somehow damaged or malformed, e.g. pages missing, or somehow "broken"; secondly, if the precis you used to make the purchase decision described something fundamentally different than what the paper delivered; third, if there was something fraudulent about the paper.

Being "incorrect" or "false" is different than being "fraudulent."