Flag burning is legal in the U.S., protected by the First Amendment.
After Trump's tweet, the spokesman for his transition team, Jason Miller, was asked about the issue on CNN.
"Flag burning should be illegal," Miller said. "The president-elect is a very strong supporter of the First Amendment, but there's a big difference between that and burning the American flag."
It wasn't clear what prompted Trump's tweet on the issue. But it came after a group of veterans and others protested this weekend at Hampshire College in western Massachusetts against a decision by the school to temporarily stop flying the U.S. flag after students allegedly burned one in protest of Trump's election.
"Today in the U.S. it's the same flag, and the nationalistic chauvinism is even worse," Johnson said.
Since the 1989 Supreme Court ruling, Congress has made attempts to ban flag burning.
The proposed Flag Protection Act of 2005, whose Senate co-sponsors included Hillary Clinton, then a Democratic senator from New York, would have made it a crime to damage or destroy the flag and would have carried a punishment of up to a $100,000 fine, a year in jail or both. The bill never came up for a Senate vote.
Around the same time, a House bill proposed amending the U.S. Constitution to authorize Congress to prohibit desecration of the flag. The 2005 bill passed the House by 286 to 130, with 18 not voting.
But the Senate in 2006 narrowly rejected a similar resolution, with the 66 to 34 vote in favor falling just one vote shy of the two-thirds majority needed. If it had been approved by Congress, the so-called flag desecration amendment would then have had to be ratified by at least three-quarters, 38, of the states.
The American Civil Liberties Union holds that flag-burning is political speech protected by the Constitution, and a senior ACLU attorney today slammed Trump’s suggestion of revoking the citizenship of a flag-burner as “fundamentally un-American.”
“The idea that the government could not only censor someone for engaging in political speech, but actually revoke a protester’s U.S. citizenship as a punishment for political speech is unconstitutional and fundamentally un-American,” ACLU senior staff attorney Lee Rowland told ABC News in a statement. “Both the protection of political speech and the inviolability of U.S. citizenship are longstanding constitutional principles at the very core of American democracy.”