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.
There is a case where I think you might have a very strong moral claim even if not a legal one: if the paper is retracted, there is no question that you ought to be able to obtain a refund.

**Addendum** One argument contrariwise: The last science needs is any further disincentive for publishers to retract papers. Maybe better for the enterprise as a whole to have a few readers get cheated than to have fraudulent and otherwise untrustworthy papers remain in the literature.