A flag is the symbol of a government and burning it is in protest to the actions of said government. My father taught me a very valuable civic duty lesson, which is one can love your country but you can absolutely despise your government. In the United States, the government does not have sovereignty. Sovereignty resides in the people themselves. Therefore, the sovereigns are telling the servant that your actions are not above reproach and you're being called on those actions due to you acting in my name without my consent.
My father was a Vietnam vet that buried 62 of his best friends during his tour over there in '66-'67.