Around 15 years ago, Louisiana passed a law that didn't ban flag burning per se, but made it legal to beat the living hell out of the scumbag who did burn Old Glory. Sadly, it was struck down in the courts.
Passing a flag burning law or an amendment to the constitution is as ridiculous as passing hate crime laws.
No one is going to burn my flag without a fight and/or having the perp arrested for destruction of private property.
There is a much bigger problem when it comes to flag burning or desecration, and that is it is impossible to truly define what a flag is.
A good question to ask those who would criminalize desecration of the flag is: Do you favor criminalizing the desecration of the holy books (e.g. the Koran or the Bible) or criminalizing vilifying religions?".
I believe that the last time I looked God commanded us to put Him ahead of all, including family and country, and most certainly our country's flag.