The American flag represents many important things in our country, but our flag is not those things. It's a symbol. The funny thing is that the flag they are burning is also a symbol for the person burning it. It stands for them just as much as it stands for the fallen soldier.
Do I want to beat the shit out of those who burn it? You bet. But once again the flag is doing it's job. A flag flying in my neighbor's yard tells me a great deal about my neighbor. In the exact same light a flag being burned by a person I've never seen before tells me everything I need to know about that person in an instant. In both cases the flag is doing it's job, and quite magnificently. In fact, if you really stop to think about it, a flag being burned is sacrificing itself, giving up it's very existence, for us, in the exact way so many brave men have done throughout history.
So my advice is to respect that burning flag to the same degree we respect a flag flying high and proud. Respect that burning flag the same way we respect those who gave up their lives for us in battle.
The Japanese bombed Pearl Harbor, killing thousands, but they did not scratch what America stands for. In fact, I dare say they strengthened our every value. You may not realize it at the time, but when you see, or even hear of, a person burning our flag, it triggers in you an even stronger sense of what that flag represents and how great our country is. That's why it pisses you off so much. In other words... the flag is doing it's job.
RIP magnificent flag. You have served your country well.