Yes, the U.S. Supreme Court has repeatedly ruled that flag burning is a form of symbolic speech protected by the First Amendment. It is a highly controversial and emotional issue, but the court has affirmed that the government cannot suppress an idea simply because society finds it offensive.
Key Supreme Court cases affirming flag burning as free speech:
Texas v. Johnson (1989): The court ruled 5–4 that the First Amendment protected Gregory Lee Johnson's right to burn a flag in protest of the Reagan administration. The majority opinion, written by Justice William Brennan, stated that the government could not prohibit the expression of an idea simply because it was offensive. This decision made flag-desecration laws in 48 states unconstitutional.
United States v. Eichman (1990): In response to the Johnson decision, Congress passed the Flag Protection Act. The Supreme Court struck down this federal law as unconstitutional, reaffirming its position that flag burning is protected expressive conduct.