Kidd spent the majority of his junior career with the Brandon Wheat Kings of the Western Hockey League. In 1989–90, He was named a WHL East First Team All-Star, the Del Wilson Trophy as WHL goaltender of the year, and won the CHL Goaltender of the Year award. He was traded to the Spokane Chiefs in 1991, and led them to the Memorial Cup championship. Kidd represented Canada three times at the World Junior Ice Hockey Championships, winning gold medals in 1990 and 1991. He also won a silver medal at the 1992 Winter Olympics as the national team's backup goaltender. Kidd played his first NHL game in the 1991–92 NHL season with the Calgary Flames, a loss to the Pittsburgh Penguins on March 3, 1992. His second game, the only other game he would play that season, was a 4–3 victory over the San Jose Sharks on April 15, 1992. Kidd stepped in full-time with the Flames in the 1993–94 NHL season, playing 31 games as backup to netminder Mike Vernon. He remained with the team through the 1996–97 NHL season. Kidd was traded prior to the start of the 1997–98 NHL season to the Carolina Hurricanes for center Andrew Cassels and goaltender Jean-Sébastien Giguère. Two years in Carolina followed; Kidd played with Sean Burke. The following year, goalie Arturs Irbe joined the team and the Hurricanes left Kidd unprotected for the upcoming Expansion Draft. After being selected by the Atlanta Thrashers in the 1999 NHL Expansion Draft, Kidd was immediately traded to the Florida Panthers. Kidd started strong for the Panthers in the first 11 games of the 1999-00 NHL season, but he was injured trying to make a save on a shot from teammate Peter Worrell during a league-mandated skills competition. This injury forced the Panthers to trade forward Radek Dvorak to the New York Rangers as part of a three-way deal with the San Jose Sharks for goaltender Mike Vernon, who left after the season for free agency. When Kidd returned from injury his play was well below NHL quality, and he was never able to reestablish himself as the team's number one goaltender. The Panthers had acquired young goaltender Roberto Luongo as well as forward Olli Jokinen from the New York Islanders for forwards Mark Parrish and Oleg Kvasha, and Luongo edged out Kidd for the starter's role in the 2001–02 NHL season. He continued to fill the backup role for one more season before being released after clearing waivers before the 2002–03 NHL season. Kidd signed with the Toronto Maple Leafs as a free agent in 2002. He followed up a 6–10–2 season in the 2002–03 NHL season with a 6–5–2 record in 15 games in the 2003–04 NHL season; his final game was a 7–2 loss to the Philadelphia Flyers in which he replaced Ed Belfour. During the NHL lockout, Kidd played with team HC Örebro 90 in Sweden. In May 2005, he signed a deal with the Hannover Scorpions in the DEL.