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: 
You can ask for anything you want, but you will not get a refund. The terms and condition of the site where you purchased it most likely clearly stated that it wasn't an option.

One example from Taylor & Francis:

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> The content in this site is provided "as is" and without warranties of any kind either express or implied.
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> Taylor & Francis Group Ltd do not warrant or make any representations regarding the use or the results of the use of the content in this site in terms of their correctness, accuracy, reliability, or otherwise.
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And another piece of sound advice:

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> If you do not agree to these terms, please do not use this site.
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More generally, the money you pay for the article is strictly for its publishing, the actual research that resulted in a "major flaw" was paid via other channels, on which it's very unlikely that you'll have any direct influence. The people making the original claim about the content of an article, and taking responsibility for it, are *the authors* not the publisher to which you paid the fee.

If you witness that a given journal has consistently low acceptance standards, make sure to notify your institution's library, they might consider resigning subscription if they gather enough similar complaints.

Sadly, for the occasional 20 bucks you consider wasted for that article (I'm sure this is purely fictional, there are many ways of getting subscription journal's content without paying for it) there are 10 unscrupulous scholars, somewhere who use 3000$ of your tax money to publish complete rubbish in an open access journal. And here the perspective of a refund is nonexistent.
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.