What about that "cruel or unusual" clause?
What punishments are unacceptable if a person has been convicted?
The 14th amendment bases its protections on "citizenship". Stripping people of citizenship and all that it entails is a bad idea and belongs in the "slippery slope" category of allowing too much creativity to the government.
We have people who pled "no contest" years ago to domestic violence misdemeanors who are now barred for life from having a gun. This is very bad direction for us to go.
The counter argument being the person who is convicted of treason, hijacking, murder, terrorism or explosives violations. I could see that such an individual be on a no fly list for the duration of their full sentence regardless of their parole. Once the time for their sentence has run, they can be removed from the list.