Flag burning is a controversial area of speech. Numerous states and Congress have tried to ban it on the grounds that it is not speech at all, but conduct. However, this attempt has always been hampered by the fact that burning is the approved and honorable way to retire a worn-out flag. Only burning a flag in anger is targeted by these statutes, which are therefore obviously attempts to punish unpopular speech.
The Supreme Court has repeatedly overturned flag burning laws. This year, a proposed Constitutional amendment to ban flag burning failed in the Senate by a few votes.
For an in-depth discussion, see my essay "The (Semiotic) Stench of a Burning Flag (Amendment)".