A lot of people have strong feelings about flag burning. It's often considered to be the ultimate unpatriotic act or even a precursor to violence. If you really want people to think you hate your country -- burning the flag will usually do it. But regardless of the social and political implications of the act, is flag burning actually illegal?
In some countries, like China, Austria and New Zealand -- yes.
Interestingly, Japan prohibits the desecration of any recognised foreign nation's national flag, but there is no law against the desecration of the Japanese flag.
However in Australia, desecrating of the flag isn't considered to be a criminal act, although changes have been attempted several times. The most recent bill to be put forward was the Flags Amendment (Protecting Australian Flags) Bill 2016 by George Christensen of the National Party.
Though flag desecration itself may not be illegal, it does need to be compliant with all other Australian laws. This can be particularly tricky when you're burning something.
For example, in one case from 2003 a person was charged with flag burning as it fell under disorderly conduct as well as violent resistance to arrest.
In 2005 a undisclosed youth was given a 12 month probation sentence after climbing an RSL flagpole and subsequently burning the flag. Although he wasn't charged for flag burning, it was for destruction of property.
So yes, you can absolutely burn the Australian flag as long as it's within the confines of the law. However, doing so in public is most likely going to garner some negative attention from the people around you.