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.
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.