It's a private property matter. If someone buys a flag, they have the right to do with it what they want.
I think flag burning promoted as an event in the public square is similar to shouting fire in a crowed theater. Both are designed to cause violence. Neither are protected by the 1st Amendment.
By the way, and not that it matters to the arguement, why are only lefty groups associated with flag burning? Conservatives get angry at government as well, yet you'll never see a them burn Old Glory.
Congress can take care of the problem by passing a law and denying the federal courts appellate review. No need for a Constitutional amendment.