Provided that the flag burner is the owner of the flag, and provided that the flag burner does not, say, throw the burning flag into a building or onto a homeless person, I don't see why there should be anything illegal about sparking up Ol' Glory.
What this leads to, however, are problems about where such activities are appropriate and how the same theories can be applied to other objects. For instance, one would have to assume that any place an American flag could be burned should also be open to people who want to burn something like a cross.
I can see some groups not liking that.
As far as I'm concerned, people should be able to burn whatever they want on their own property (as long as it's small-scale enough not to poison the neighbors or destroy surrounding property, and as long as they don't try to collect insurance off it). This includes flags, crosses, pictures of Bill Clinton, pictures of Jesus Christ, Windows 2000 boxes, whatever.
I'm not sure what the regulations are for burning things on public property and government property. But I think that anywhere a comparably sized piece of cloth is legal to burn, a flag should be considered open season.
It's all about protecting free speech, from Buddhist monks to radical university activists to the KKK. If you don't like what someone is saying or how they choose to express it, tough shit. As long as they aren't committing an actual crime (such as threatening people), people have the right to be as stupid, or, in the case of flag burning, unoriginal as they want to be.
Let's face it: people have died for the flag and what it stands for. Imagine how you would feel if your buddy died in 'Nam and was laid to rest in a coffin covered with that flag -- and then you see someone burning it. I think folks should absolutely have the right to exercise their speech in that manner, but think twice before you decide that it's the proper way to protest your school's fetal pig dissection.