Flying, that is not a constitutional right.
Buying a gun is, however.
That means that someone on these watchlists could be stopped from flying or made to go through extra screening but not stopped from buying or carrying a gun. What is the difference between flying and carrying a gun? The gun is included in the constitution. If constitutional rights may be taken away through just putting someone on a list, that means that not only your 2nd amendment rights may be taken away, but also your 1st amendment rights and all the others you were guaranteed in the bill of rights and the rest of the constitution.
We all know that sometimes your rights may be taken away, but how do you determine when a right may be taken away and when a right may not be taken away? You use due process. Due process includes things like whether the cases was decided by a judge or an administrative employee, the value of the thing being taken away (constitutional rights are very valuable), and whether or not the defendant was able to present rebuttal witnesses.
You can be put on the no-fly list for many things, such as repeated travel to certain countries, saying something on social media, having a similar name to someone else who was put on the no-fly list, or being suspected of criminal activity other than terrorism. The problem with all these is that there is no due process. Anyone could be put on the list.
Like I earlier stated, do you really want the government to be able to take away your constitutional rights simply by placing you an a list? I don't.
If the left wants to make it so that people on the no-fly list cannot buy or carry guns, that is fine, but first they have to fix the glaring due process issues with being put on the list. If there was proper due process, nobody would have a problem with people on the no-fly list not being able to buy a gun because the only people on the list would be people who were proven to be the 'bad guys'.