Conclusion: Although the world as a whole has seen a positive Flynn effect in the past few decades, there have been multiple studies that show a negative Flynn effect in a few places. Dutton and Lynn are real scientists who wrote several of these studies. The scientific community appears to accept their basic finding, i.e. that the negative Flynn effect exists sometimes.
Lynn has been accused of using this and other research to promote scientific racism. In my opinion Dutton and Lynn's explanations of their findings certainly seem prejudiced against immigrants and women. If anyone were to cite their studies in a political argument, or advocate for any kind of public policy based on their research, I would be very skeptical.
"I would like to know if such studies have any kind of credibility."
This is a great skeptical reflex, but it is also difficult to define exactly what has credibility and what does not. When I see a surprising result, there are a few things I can check to see if I should take the source seriously.
1. Read the original scientific article. Does it follow the norms and standards of scientific work?
The original article is written in plain English and it appears to be a proper scientific article. It references other similar science on the topic, and does not appear to overstep its conclusions.
It presents data that was taken when the IQ test for France was renormalized, and points out some interesting declines in the data. Most of the discussion section is spent on informed speculation about why those declines might have happened. Their speculation is clearly indicated by repeated use of words like, "might" and "may be."
Note that you did not link to the original article, you linked to "A comment" on the original article. The comment appears to be a scientific article in itself.
The same authors wrote a review paper where they look at a negative Flynn effect in 9 studies (comprising 7 countries). They examine 4 possible causes of the negative Flynn effect, but are unable to give evidence for any of them, a frustration I can relate to after researching many lackluster skeptics.se answers.
The four proposed causes were, immigration from low IQ countries, an increased number of women in IQ tests (they claim women score 5 points lower), dysgenics (low intelligence people having more babies), and an older age of fatherhood.
In this paper, they also remind readers that there are still many positive Flynn effects.
In the present study, we must emphasize that even though we identified several studies showing a decline in IQ, there is currently still a much larger pool of studies showing an increase in IQ. ... Moreover, in their recent meta-analysis, Pietschnig and Voracek (2015) confirmed the 3 points per decade average increase in IQ. Therefore, it is imperative to discuss our negative Flynn Effects in the light of the positive Flynn Effects findings in the literature.
These negative Flynn effect findings do not represent a general trend.
2. Check the credentials of the authors. Are they real scientists? Have they published in this field before?
Dutton and Lynn have published multiple studies on negative Flynn effects and intelligence. (Note that not every paper in that google scholar link is by them.)
Dutton is a Professor at University of Oulu, and the president of a think tank, the Ulster Institute for Social Research. Richard Lynn is a professor emeritus of psychology at the University of Ulster. Wikipedia notes that:
Lynn sits on the editorial boards of the journals Intelligence, Personality and Individual Differences, and Mankind Quarterly, which has been called a white supremacist publication. He is also on the board of the Pioneer Fund, which funds Mankind Quarterly, and has also been described as racist in nature. A number of scientists, including Leon Kamin, have criticised Lynn's work on racial and national demography and intelligence for lacking scientific rigour and for promoting a racialist political agenda. A number of people, such as historian of psychology William Tucker, have said that Lynn is associated with a network of academics and organizations that promote scientific racism.
For what it is worth, these guys are real scientists. The meta-analysis by Dutton and Lynn, cites 9 papers total, 5 of which come from the allegedly racist journals that Lynn helps edit, Intelligence and Personality and Individual Differences.
A brief tangent about science and racism
While I was reading his papers, I picked up on a thread of racism and sexism. One of his explanations for the lowering IQ scores is that immigrants from low IQ countries are bringing it down. Another is that women are bringing it down, because women do worse on IQ tests. I also ran across an article he wrote about racial difference in IQ. When I saw the accusations on Wikipedia, I was not at all surprised.
I am not qualified to judge the evidence on its own merits. When I sat down to research this topic, I did not expect to encounter the specter of prejudice, and his racist views are only sort of relevant to the claim. Calling one of the authors racist or sexist is an ad hominem attack, but it also seems relevant. Prejudice is by definition coming to a conclusion before seeing evidence. The Wikipedia article presents quite a bit of evidence. A discussion of how sexism, racism and science interact is a rabbit hole with no end, and only tangentially relevant to the claim.
I should probably acknowledge my own prejudice; when someone starts making claims about the relative abilities or merits of certain groups my skepticism increases dramatically.
3. Look at how other scientific articles cite their work.
Although I am not qualified to judge their methods and conclusions, other scientists are. If his methods are not sound, or if his data don't support his conclusions, other authors will either not cite him, or cite him negatively. Unfortunately it can take a couple of years for these articles to be researched, written, and published. I don't expect anything published in the last few years to have more than a handful of citations. I found a similar, slightly older, paper by Dutton and Lynn, that has had more time to garner citations.
If, as William Tucker claimed in the Wikipedia article, Lynn is "associated with a network of academics and organizations that promote scientific racism," that network will give him some positive citations. Because the Journal Intelligence was accused of being a haven for racist science, I will not look for positive citations there. I will similarly exclude Personality and Individual Differences, because Lynn sits on its editorial board. I have no way of knowing if the journals I have been looking at are similarly accused.
I did not do a exact count but roughly half of the citations of this paper come from those two journals. It seems that the research on a reverse Flynn effect is concentrated in a few journals that have been accused of scientific racism.
Articles, (A,B,C,D,E,F) only briefly cite the article, giving it one sentence or less. Every article I read the citation in repeats Dutton and Lynn's conclusion briefly, but uncritically. There are more articles that I could skim, but I am not going to spend all day on this. It appears that the scientific literature accepts that a reverse Flynn effect is happening in some places.
Conclusion: Although the world as a whole has seen a positive Flynn effect in the past few decades, there have been multiple studies that show a negative Flynn effect in a few places. Dutton and Lynn are real scientists who wrote several of these studies. The scientific community appears to accept their basic finding, i.e. that the negative Flynn effect exists sometimes.
Lynn has been accused of using this and other research to promote scientific racism. In my opinion Dutton and Lynn's explanations of their findings certainly seem prejudiced against immigrants and women. If anyone were to cite their studies in a political argument, or advocate for any kind of public policy based on their research, I would be very skeptical.
