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. When he was five, he began playing youth soccer, and attended John F. Kennedy High School where he played on the boys' soccer team. After graduating from high school, he attended Hartwick College for a single year. Despite playing 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.