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: 
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.
If you are just looking to get your money back, then I am afraid it is not worth an effort; you probably will spend more on the telephone calls than they charged you for the article.

However, it could be nice to set a precedent like this: to request a refund and eventually to sue a lazy publisher, who do not bother to introduce a proper level of scrutiny in their peer review process, and instead charge the authors to publish some bogus papers and then charge the readers to access them. I have no idea whether or not such a case can win (and I guess it depends on jurisdictions). The question just adds to the bigger question of very complicated relations between academic publishers and academia.