To me, burning a flag is symbolic indeed, a protest against something. As others have pointed out, the flag is piece of cloth and if burning this cloth-symbol best depicts what they protesting against, well then they should burn it. It however, tells a lot about their skill in pointing out what is wrong and their ability to protest against that in particular.
However, I would fiercely defend their right to protest against what they think is wrong.
Someone raised the point of not doing this out of respect for soldiers of wars and the like.. to me, those soldiers didn't fight for a flag, they fought for what the flag represented at the time (if they indeed had any choice at all, which is rare), if the politics and situation in a country has changed, the flag now represents something different, thus, it is the representation of the flag that is in question, not the flag per say. So by burning a flag that today represents one thing doesn't mean that one dishonors what that flag stood for previously.
As for, Australia being the best country.. nah, only someone who haven't travelled a lot would say such a thing. I choose to live here because it is good overall and better then a lot of others in some areas, but it is certainly worse off in other areas, albeit they don't happen to be that important to me. In essence, there is no such thing as a best country that is best for everyone. In my travels, I have frequently encountered people stating that they live in "the best" country, and when probed for their comparative reference points, mostly they're not well traveled, have only been to a select few other locations and only as tourists. From a material point of view, yes, Australia is great.. from a work/life balance and security of welfare, not so great. From a climate point of view, great.. from a sustainable climate point of view, horrific.
I would hate Australia going down the path of patriotism to the point of critiquing something within the politics or people of Australia means that you are anti-australian.. Only countries with big flaws adopts such a mentality. The others realize that from critique comes growth.
Sorry if I derailed the topic a bit, but it bugs me when people use terms like "best" in a patriotic sense. It is like stating that someone is the Best guitarist.. there is no such thing LOL.. they can be extremely good at what they do in a particular style or reasonable good all around player, but BEST, they are not as it doesn't exist.