I think it's worth noting that due process of law is fairly often used to restrict or prevent US citizens from buying or owning firearms. Fully automatic weapons and silencers are very expensive to license, and not everyone can have them. Convicted felons and illegal aliens are generally prevented from owning firearms. Courts can find grounds such as domestic violence for preventing firearm ownership.
In some (few) of these cases, no one has been accused or convicted of a crime, yet their rights are restricted. Although few, such examples indicate that rights can be restricted. However, there appears to be due process involved in all of these examples.
The current direction of US laws seems to be in favor of broader rights of concealed carry, and more ability to carry firearms in a wider variety of public and privately-owned areas.
Perhaps the point is that no due process has been carried out in terms of the no fly list. What about someone on the no fly list wanting to travel with a group? Is denying them air travel equivalent to restricting their freedom of assembly, another constitutionally guaranteed right? (I'm rather surprised no one has tried that argument.)
I don't want to get into too many "what if" arguments, just to point out that somewhere, we need to get a handle on the type of person owning and using firearms. If firearms don't kill people, but their owners do, then we need to get more control of ownership and access. We can respectfully disagree about whether the no fly list is a place to start. I think it's a worthwhile effort even if the best it does is contribute to an ongoing discussion that has any nuance at all.