I like flag-burners about as much as I like cross-burners, but as satisfying as it might be to strip them of their citizenship, what both groups are doing is protected free speech. As long as the cross burning is not explicitly aimed at someone as a terrorist act, it is available as a form of expression. Flag burning is much the same. Odious speech is protected not because it is worthy or interesting, but because protecting even odious speech is the best way of protecting more valuable speech.
What I do find interesting is that Trump considers loss of citizenship a punishment on par with a year or so in jail. That suggests he thinks of citizenship as not being especially valuable. So you lose your citizenship, then what? Presumably, you become a legal resident without voting rights. You go to the back of the line, and in seven years you can re-apply and take the test to prove you're worthy of being taken seriously? It's like a time-out to teach better citizenship, in other words.
Well, maybe. The alternative would be exile, but that's dubiously constitutional even at the state level. On the other hand, if we're obviated First Amendment protections and are stripping citizenships, who knows if the prohibition against exile would hold?