Burkett first represented Australia at the 1987 Pan Pacific Para-Swimming Championships, where he won a gold medal in the 100 m butterfly. At the 1988 Seoul Games, he won a silver medal in the Men's 4 × 50 m Freestyle Relay A1–A8 event. At the 1992 Barcelona Games, he won a bronze medal in the Men's 50 m Freestyle S9 event. He won a silver medal at the 1994 Victoria Commonwealth Games in the Men's 100 m Freestyle S9 event. At the 1996 Atlanta Games, he was the captain of the Australian Paralympic team. At the games, he won a gold medal in the Men's 50 m Freestyle S9 event, for which he received a Medal of the Order of Australia, and a silver medal in the Men's 4 × 100 m Freestyle S7–10 event. At the 1998 IPC Swimming World Championships in Christchurch, he was part of the Australian team that won a gold medal and broke a world record in the 4 × 100 m Freestyle Relay event. He won a gold medal and again broke a world record in the Men's 50 m Freestyle S9 event at the 1999 European Championships; his father had died earlier that year. He carried the Australian flag at the opening ceremony of the 2000 Sydney Games. At the Games, he won a silver medal in the Men's 4 × 100 m Freestyle 34 pts event; he was very disappointed that he could not defend his 50 m freestyle title. He retired from competitive swimming after the 2000 games.