The no fly list is one of "those things" that's visible to the public,
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yes and no.
The existence of the list is common knowledge.
Who is ON the list is not.
What the specific criteria are to be put on the list, are not, either.
We are left to assume, or infer, that it is the "bad guys" who get on the list, but unfortunately, without some kind of oversight, we don't KNOW.
As far as I know, we don't have any PROOF of ANYTHING other than there is a list, and if you are on it, you can't get on an airplane in the US.
We hear, once in a while, of children, the extreme aged, and other innocent people being on the list, and its always explained away as a "mistake". Similar name, or something like that.
I can see SOME logic in having a list of known terrorists, and keeping an eye on them. A "secret" list?, one we don't know what it takes to be put on, with no clear method for legal challenge if you are put on the list "by mistake"?
I have never thought that to be the best of ideas.
As for the no fly list having precedence over the US Constitution? Not in any normal legal sense as far as I can see. US LAWS, passed by Congress and signed by the President DO NOT supersede the Constitution. NO Agency regulation supersedes the Constitution. Certainly no administrative LIST should be considered superior to the supreme law of the land.
I feel confident that is what the courts would rule. However, individuals in the Executive branch might feel differently, and do as they please, until the matter is resolved in court, and they are ordered to do otherwise.
We don't have a perfect system.