The country does not need to regulate the burning of the U.S. flag. What is does need is a Rick Monday national holiday. In 1976, Chicaco Cub outfielder risked his well-being to rescue the American flag from some flag burners.
While I believe the 1st Amendment protects a person to burn the flag, it also protects the person who prevents a flag from being burned.
Only if they didn't legally own the particular flag they were going to burn - if they owned the flag legally then his 'rescuing' the flag was stealing and thusly violating their property rights. Stealing is not protected under the first amendment.
If however the flag was public property or private property of someone not consenting to having the flag burned then he was definitely doing something lawful, and his civic duty if it was public property.
Your point is well-taken.