Banning the message, not the act
A quick note on flag burning:
The flag, when it is in such condition that it is no longer a fitting emblem for display, should be destroyed in a dignified way, preferably by burning.
Source: https://www.law.cornell.edu/uscode/text/4/8
Not only is flag burning not illegal, it is the preferred method of disposing of a flag in the U.S. Flag Code. What is being discussed in banning "flag burning" is not burning itself, but burning with specific intent or to send a specific message.