Flammini began competitive racing in 1973, contesting the Italian Formula 3 championship in a Brabham BT35 and a March 733 powered by Ford TC engines. He finished seventh in the championship with one win and two podiums across six races.
He progressed to the European Formula Two Championship in 1974, entering with Equipe Nationale in a March 742-BMW, and finishing 16th in the standings with 2 points. In 1975 he raced for Trivellato Racing Team and Project Three Racing across a combined programme, finishing 6th in the championship with 22 points, one win, and four podiums.
The 1976 season brought his strongest Formula Two campaign. Racing for the March works team in a March 762-BMW, Flammini took two wins — at Thruxton and Rouen — added two pole positions, three podiums, and finished 6th in the European championship with 26 points. He also won the Italian Formula 2 championship that year. In 1977 he competed with the Scuderia Gulf Rondini and Fred Opert Racing programmes but scored no championship points. He returned to Formula Two in 1979 for Sanremo Racing, scoring one podium and 4 points, and ran a self-entered Ralt RT2 in 1980 without points.
Outside single-seaters, Flammini made a non-championship Formula One appearance at the 1975 Race of Champions at Brands Hatch in a Williams FW02, though he did not start. He contested the 1981 24 Hours of Le Mans for Scuderia Supercar Bellancauto in a Ferrari 512BB shared with Fabrizio Violati and Duilio Truffo, but the car retired after 118 laps.
He was Italian Touring Car Champion in 1987, and holds Monza lap records in three categories: Formula 3, Formula 2 (set at the 1980 European Championship), and Supertouring (set in 1990 in a Sierra Cosworth). He also won races in sports car competition with the Chevron Sport 2000 BMW for the Genovese Racing Team during the 1980s.
Flammini founded Flammini Racing in 1975, a motorsport management and promotion business that would evolve into the FG Group. The organisation became involved in marketing for both car and motorcycle sport events and motorshows. From 1983, the FG Group's motor racing programme was carried out in collaboration with the Italian Motorcycling and Car Federation, contributing to the promotion and economic development of Italian national motorsport.
Corporate ventures included co-founding Octagon Motorsports with the Interpublic Group of America, and Infront Motorsports, among other international motorsport organisations.
Flammini's most lasting contribution to motorsport was the creation of the FIM World Superbike Championship. Under his FG Sport organisation, the championship ran its inaugural season in 1988. Under his stewardship the series grew to become one of the two leading motorcycle road racing championships globally, drawing participation from as many as seven major motorcycle manufacturers and reaching a worldwide audience across more than 120 countries, where it competed with MotoGP for viewership and manufacturer interest.
Later career appearances included the 2004 Italian Superstars Championship, where he finished 8th with 8 points.