I think it does come under freedom of expression: (as much as I loathe your message, I'll defend to the death your right to do it- paraphrasing). As much as it pains me to think of ignorant hippie punks trashing America, they do it in a thousand other ways, so it's a futile gesture to outlaw one. And I think proponents of an Amendment make the mistake of holding a symbol for something more sacred than the ideals it stands for, much like (on a more dramatic scale) killing others for disrespecting a holy site or symbol of a religion.
In general, Constitutional Amendments have the purpose of enshrining freedoms, not restricting them, except for the ill-fated Prohibition. Restricting freedoms should be done with utmost caution, and where feasible by States or localities.
Yet when those hippie punks burn a flag, aren't they begging for our freedoms to be outlawed? "...and to the Republic, for which it stands..." The flag is representative of our nation, our laws, our freedoms. When one chooses to destroy the flag, he is essentially saying "Turn my freedom to ash." A flag isn't just a thing, really, no more than a crucifix is just a thing. They are something more because they represent something much larger.