Henrik Flöjt made his international début at the 1975 World Championships, where he won a gold in the relay. At the 1976 Olympics, he won his second and last international medal, a silver, again in the relay. Individually his best place at an international championship was fifth in the 10 km at the 1976 World Championships. Domestically Flöjt won one individual Finnish title in 1975 and one individual Finnish Championships bronze, in 1977, both in the 10 km, and two Finnish relay titles, in 1972 and 1975. His older brother Heikki was also a biathlete who competed at the 1968 Winter Olympic Games and won a relay silver at the 1974 World Championships.