Kinnear moved to the United States with his family when he was three years old. He grew up in Fremont, California, which he considers to be his hometown. He began playing youth soccer at the age of five before attending John F. Kennedy High School where he played on the boys' varsity soccer team. After graduating from high school, he attended Hartwick College for a single year. As a defender, he scored three goals as Hartwick went to the Final Four.
In 1989, Kinnear signed with the San Francisco Bay Blackhawks of the Western Soccer League (WSL). Kinnear remained with San Francisco Bay as the Blackhawks became one of the dominant teams of the era. In 1990, the WSL merged with the American Soccer League (ASL) to form the American Professional Soccer League (APSL). That season Kinnear again earned All Star honors. In 1991, the Blackhawks took the APSL title and in 1992 went to the semifinals of the CONCACAF Champions Cup. Kinnear again earned All Star honors in 1992. In 1993, the Blackhawks owner pulled the team from the APSL and moved it to the lower division USISL, renaming the team the San Jose Hawks in the process. Despite the move to the lower division and a winning season, the Hawks folded at the end of the season.
In 1995, Kinnear played a single season with Mexican First Division team Necaxa. That season, he became the first U.S. player to score in the Mexican First Division. Necaxa also took the Mexican League title.
In 2001, first-time head coach of the San Jose Earthquakes, Frank Yallop, named Dominic Kinnear as his assistant coach. Together, they helped coach the Earthquakes to the MLS Cup in 2001 and 2003. In 2004, Frank Yallop left to coach the Canadian national team and Dominic was promoted to head coach of the Earthquakes, assigning John Doyle to replace him as assistant coach. After leading the Quakes to the MLS Supporters' Shield in 2005, Kinnear moved to Houston with the rest of the Earthquakes, when the team was renamed the Houston Dynamo. On November 12, 2006, Kinnear led the Houston Dynamo to their first MLS Cup Championship. On November 18, 2007, the Dynamo won their second MLS Cup in a row, again beating the New England Revolution. Kinnear resigned as head coach of Houston Dynamo effectively as of October 25, 2014, after their last match of the regular season.
Kinnear became the new head coach of San Jose Earthquakes following the conclusion of the 2014 regular season He replaced Mark Watson, who was fired on October 15, 2014.Ian Russell took over for the final two matches of the 2014 regular season on October 19 and October 26.