Donald Trump tweet Tuesday:
"Nobody should be allowed to burn the American flag -- if they do, there must be consequences -- perhaps loss of citizenship or year in jail!"
Contrary to President-elect Donald Trump's tweet, even if flag-burning weren't protected by the First Amendment (and it is), you couldn't strip people of their citizenship for it.
Let's begin with the constitutional text, here from section 1 of the 14th Amendment:
"All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside."
Once you have American citizenship, you have a constitutional entitlement to it. If you like your American citizenship, you can keep your American citizenship -- and that's with the Supreme Court's guarantee, see Afroyim v. Rusk (1967):