Disclosed is a flame-retardant polyester polymer dyeable with a cationic dye, a method of producing the same, a copolyester fiber using the same, and fiber products using the copolyester fiber. In the method, after a dimethyl isophthalate component containing metal sulfonate of Formula 2 separately reacts with ethylene glycol so that an extent of the ester interchange reaction is 95% or more to synthesize bis(hydroxyethyl terephthalate) containing metal sulfonate of Formula 3, bis(hydroxyethyl terephthalate) is fed so that a content of bis(hydroxyethyl terephthalate) is 0.01-5 mol % based on a diacid component in a polymer in a course of producing polyester, a phosphorus-based flame retardant of Formula 1 is fed so that a content of a phosphorus atom is 500-40000 ppm based on the polymer, and the mixture is copolymerized. The polyester polymer is dyeable with cationic dye while having excellent flame retardancy, and can be melt-spun like other polymers capable of being melt-spun. The copolyester fiber using the polyester polymer is capable of being processed according to processes through which conventional polyester fibers are processed, and is dyeable with cationic dye while having excellent flame retardancy.