Brockenshire was born in the Melbourne suburb of Prahran and lives in the Northern Rivers of New South Wales. He was born without a tibia and a shortened femur on his left leg, and at the age of eighteen months, his left foot was amputated. He began swimming at the age of about ten to improve his fitness. He won medals in able-bodied surf lifesaving competitions and was the state surf ski champion in 1987. He was inspired to take up competitive swimming after watching the events for people with disabilities at the 1994 Victoria Commonwealth Games in Canada.