Real answer: The First Amendment of the United States Constitution prohibits the government from "abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances."
In the American political system, the U.S. Supreme Court is the authoritative interpreter of what the Constitution means. In the case of flag burning, the Supreme Court has interpreted laws prohibiting flag burning as "abridging the freedom of speech." The Supreme Court explained its reasoning in 3 different opinions dealing with different nuances of the question, if you are curious about its thinking:
Street v New York -
https://supreme.justia.com/cases/federal/us/394/576/case.html
Texas v. Johnson -
https://supreme.justia.com/cases/federal/us/491/397/case.html
US v. Eichman
http://www.letsrun.com/forum/post.php?board=1&reply=6160886
Unless the Supreme Court can be convinced to change its mind, the only way to reverse the Supreme Court would be to amend the First Amendment.
That's why America allows the burning of its flag in its country.