Australian patriotism and American patriotism are different.
Americans show their patriotism by displaying their flag wherever they go: in business and even in their front yard. Whereas Australians show our patriotism by refraining from displaying our flag day to day and reserving its display for formal occasions and formal institutions.
So to Australians American patriotism looks shallow and even exploitative, while to Americans Australians seem unpatriotic and laconic.
And while Americans allow the burning of the American flag, to burn the Australian flag would be a faux pas.