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Recently, I came across a PhD thesis and an article derived from that PhD thesis and found a serious flaw in them that actually makes their conclusions invalid. In the first place, I was unsure if I'm right or not, so I contacted the guy that wrote the PhD thesis and subsequent article and described my concerns and I showed my calculations to him and asked if he thinks in fact there is a major problem in his PhD thesis and that article, which is derived from it. He responded back that embarrassingly, in fact I'm right and there is a problem but he can't do anything about it. I didn't want to force him to do something but I'm just thinking maybe there might be a possibility to publish an erratum for at least that article. It's a major flaw and unfortunately it just invalidates the major conclusions of paper and PhD thesis. Surprisingly, the article is cited for 15 times and nobody found that obvious problem. My question: What's the best way to deal with these kind of situations that even author himself/herself admits that in fact there is a major flaw in his/her thesis or article? I appreciate any suggestion or recommendation.

One possibility is for you to write a paper on your reanalysis. Often this would need to be something more than pointing out the flaw alone, but that may be discipline-dependent. If the flaw you have detected is a key part in your own analysis of your work, including your updated analysis in a larger article (while citing their paper) is a smooth way to point out how you had to change the method.

The second possibility is that many journals (at least in my area) allow for Comments on articles they have published. These are for just this purpose - to point out something 'wrong' about a paper that has been published. If the editors decide to proceed with it, the original authors are usually given an opportunity to craft a Reply piece to agree, disagree, alter, whatnot. Then they are published back-to-back in the journal.

Do not overthink it.

I have had similar experience and authors were reluctant at first (mostly because they have moved to another problem).

It is very dangerous to leave a flaw in the literature. Especially a critical flaw where others may build on it. This will lead to more chaos. I am aware some (well-known) people do not care about their old results being incorrect. But this is not what Academia is about. You should appreciate the peer review and rigorous findings more than anything else. You already have contacted the author, offer him a collaboration (if seems right) on correcting the whole thing in the context of your work.

You usually have spotted the error because your work is related. On that particular connection re-analyze the claim and correct it. Include in your new paper the claim, prove why it is incorrect and prove the new correct result. This actually can be seen as a new contribution to your paper/thesis.

For me, I was very satisfied with the outcome; the first author of the other paper did mentor me for a while after we met at a conference.