This flag was flown by John Bowman on his farm Archerfield, Richmond NSW, after receiving news of the victory of the Battle of Trafalgar reached NSW in April 1806. The flag is the first recorded use of the kangaroo and emu as supporters of a shield, and may be the origin of their use on the Commonwealth Coat of Arms. 
An account of the battle and victory, on 21 October 1805, was published in The Sydney Gazette on 13 April 1806. A day of thanksgiving was ordered by Governor King for the following Sunday at which 'all persons not prevented by sickness or the necessary care of their dwellings are expected to attend.'
According to the Bowman family, the flag was made either by Mary Bowman, John Bowman's daughter, from her mother Honor's wedding dress, or by Honor Bowman, John's wife. Mary, born in 1797, was aged nine years at the time.
It is unlikely that Honor or Mary Bowman painted the image, which appears to be the work of a professional sign painter.