A group of protestors was arrested after they acted violently by burning the American flag and destroying public property. They claim their actions are protected by the First Amendment. Do you think their defense will be successful?

The First Amendment of the United States Constitution offers protections for certain types of speech and expression. Only some of the actions taken by the protesters fall under the protections of the First Amendment. Americans have the right to freedom of religion and freedom of expression that is free from government interference, provided those expressions do not violate any existing laws. The First Amendment allows the government to prohibit speech that causes a breach of the peace or results in violence. By destroying public property, the protesters clearly violated this aspect of the Constitution and their attempt to use the First Amendment as a defense will not likely be successful in this regard.
The Right to Assemble
The right to assemble is a primary component of the First Amendment, but it is often misunderstood. Americans have the right to gather together for "peaceful and lawful purposes." Any demonstration that results in violence or causes a breach of the public peace is not a protected form of protest. The government may also prohibit Americans from gathering in groups that are known to promote illegal activities.
Flag Desecration Law
The U. S. Supreme Court has determined that the Constitution's First Amendment does afford protesters the right to desecrate the American flag. It is believed that outlawing such practices, while they are generally regarded as offensive, would do greater damage to the country legally and ethically than allowing flag burning to take place. While Congress has attempted to pass anti-desecration laws on many occasions, it has not been successful at convincing the Supreme Court of the constitutionality of these laws. Burning the flag is considered an act of political expression and thus, as long as it is not accompanied by violence or other disorderly conduct, is not a criminal activity in itself. The protesters burned the flag in the process of illegal conduct, however, so they will not likely be successful in using the First Amendment to defend their actions.
Landmark Cases
The 1989 case of Texas v. Johnson began when Gregory Lee Johnson burned the American Flag in protest. He was arrested and charged with violating a Texas statute that covered the desecration of all venerated objects, including the nation's flag. Johnson appealed on the grounds that his actions were protected by the First Amendment, and the Supreme Court agreed. One year later, the United States v. Eichman case confirmed this ruling on a federal level.
While the protesters can successfully argue that their flag burning was protected under the First Amendment of the United States Constitution, the First Amendment does not protect their other actions. Violence, damaging public property, and disturbing the peace are criminal acts that are punishable by law, and protections for protesters only extend to peaceful and lawful assemblies.
https://www.law.cornell.edu/wex/first_amendment

https://www.uscourts.gov/educational-resources/educational-activities/facts-and-case-summary-texas-v-johnson

https://www.uscourts.gov/educational-resources/educational-activities/texas-v-johnson