Flemming Davanger came from Bærum and starred in curling from an early age, competing three times for Norway at the World Junior Championships, winning a silver medal in 1983. Davanger played third early in his career but moved to second in later years. He had a long career, winning a bronze medal at the 1986 European Championships and winning the European Championship title in 2005. Davanger won three medals at the World Championships, with silver in 2002 and bronze medals in 2001 and 2003.
In 1992 Davanger was on the Norwegian rink that placed second in the curling demonstration sport at the Albertville Winter Olympics. The highlight of his career came in 2002 when Davanger played on the Norwegian rink that won the Olympic gold medal at Salt Lake City. He was also on the Norwegian curling squad at the 2006 Winter Olympics, placing fifth.