Flag Burning Amendment Fails
66-34... pretty damn close
My main point is that something like burning the flag should never be banned. Though you and I may find it reprehensible, it is necessary for open and robust discourse. Open and robust discourse is the exact purpose of the First Amendment. Also, if you look at the history of what we call "free" speech (I use quotations b/c much speech is not free), you'll see that there exists a hierarchy of speech and the protection of that speech correlates to where it falls in that hierarchy.
Flag burning is considered "political speech." Political speech is the MOST protected form of speech. So if this were a Supreme Court decision (and it was in 1984) the Supreme Court would show deference to the speech. The thought is that you err on the side of letting too much in, rather than censoring too much out. This thought process is indicative of Oliver Wendell Holme's "marketplace of ideas" theory. Which in its most crude form, basically says, throw everything out there and let society deal with it. The better the idea, the more reverence society will pay it; thus it will rise to the top. The worse the idea, the quicker it will sink. It's basically derivative of capitalist thought but generally tends to work for speech.
So in the end, I say all this only to say that the ability to express your political views in the manner you see fit (so long as it does not infringe on other's rights) is one of the proudest traditions this country possesses. To take that away just because you find the action reprehensible is antithetical to American Constitutional thought/ideology. You cannot practice viewpoint discrimination when concerned with the methodology someone chooses to espouse their views.
HOWEVER, if Congress is able to pass the amendment and get it ratified by 38 of the 50 states, so be it. The voice of the people has spoken and that is exactly how you're supposed to do it Constitutionally. I would back that.