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: 
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.
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."