Okay, here we go again on this subject...
First of all, let me state that i don't hold a particularly strong conviction either way on this issue. I can definitely connect with the views held by both sides on this one. And before anyone out there asks, my personal political mindset is strongly conservative, with a healthy dash of libertarianism thrown in for good measure. So there, everyone knows exactly what side i'm on - although i think in the case of this issue, it's one that transcends simple right/left wing thinking. I think i could find just as many people on either side of the aisle, to agree with either of the alternatives, either in whole, or in part. 
Whatever your viewpoint on the subject, i am surprised that so many people that would never, ever burn a flag are so very passionate about having the right to do so. That is strictly an observation, not a judgement. 
Okay, now, back to the issue at hand. First of all, i don't care which end of the argument you support, we need to get back to some good, grounded logic in our arguments. First of all, the proposition at hand, is that of a Constitutional amendment, which would allow for flag burning to be considered a legal offense. That means exactly that - if such an Amendment were to pass, the question of whether or not flag burning would be a form of free speech or not would therefore be rendered moot.  And to those that said that this would require the appeal of the First Amendment, no it would not.  An amendment does exactly that - it modifies and superceeds what came before it. 
In this case, i'm pretty certain that it would be worded such that the Amendment would specify flag burning as a singular act that would no longer be considered an act allowing for First Amendment protection. It would not invalidate the rest of the First Amendment. If anything, it would clarify the First Amendment, and what is and what is not exactly free speech. In this case, the one singular act of flag burning would be judged not a Constitutionally protected act of free speech. It would (presumably) say nothing at all about any other act or expression of free speech, so it would certainly not nullify or repeal the First Amendment. Let's follow the rules of logic here at least... 
Secondly, bringing Jane Fonda or Vietnam into this argument is a red herring, plain and simple. I think it's a stretch personally to call the act of flag burning an act of treason. I realize others may feel differently, but let's keep to the discussion at hand. Flag burning... offensive - yes. Treasonous ?  Personally, i think not. 
Next.... 
"The issue generally comes up when Republicans, whose core values are with their funders, look for issues of passion to paste over what would otherwise be glaringly obvious and garner very few votes."  and
"Free speech has always been difficult for authoritarian right wingers to handle, hasn't it?"
Ummmm... i don't remember anyone before you bringing political parties or viewpoints into the picture. I am personally neither a Democrat, nor a liberal, but i haven't insulted those who are. Could you give those of us whom you might consider ourselves to possess the conservative viewpoint the same courtesy?  Enough said, i think. 
Going on....
"instead of passing a law to burn flag burning, how about we repeal some laws that cause people to want to burn flags?"  
Possibly because i doubt we would ever come to a concesus in this forum, much less the country as a whole, exactly which laws we should repeal? 
Next issue... do rights have limits?  Of course they do. And putting limits on rights in no way diminishes the original right. Let's say, for sake of argument (and yes, i know i'm exaggerating), your personal choice for exercising your right of free speech was to insert a flaming hamster into your ass and sing "porgy and bess."  If that's your thing, so be it - but by the same token, don't expect us to allow you to do it on stage at a Kindergarten pep rally. We as a people insist on some reasonable restrictions on rights, so as to prevent chaos. No right is absolute, and the Constitution was written vaguely, so that the citizens could use their God-given common sense to figure things out, without every single contigiency being spelled out. So therefore, it is a reasonable exercise to ask this question about flag burning. So don't dismiss out of hand the arguments that those in favor of such an Amendment are elaborating. 
Bottom line for me is this... I think it sounds wonderful in theory. After all, who could be opposed to something (seemingly) so obvious as protecting our flag from being desecrated?  I would be concerned about the very real, but in reality very slight, loss of a bit of our personal freedoms to express our beliefs. 
In the end however, i don't think it would be even remotely practical, even if i came to the viewpoint that it was a good idea in the first place. I won't rehash them all here, just one for an example, how would you define "a flag?"  Would it be okay to burn a photograph of a flag, etc.?  You see how it sounds good (potentially) on paper, but fails the practicality test in the real world.
My personal take on how to handle flag burners?  I think they are scum, who cannot win on force of their arguments, so they resort to symbolism such as this, as a last-ditch effort to turn the tide in their favor. I say we view them properly, exactly as they have demonstrated themselves to be, in using the right of free speech to give them cover for their acts.  Ostracize the bastards, and let them and their views rot. If their views were to be taken seriously, they would not need to resort to burning a flag in the first place.