Kinney made his feature film debut in 1985 playing a burnt out Peace Corps volunteer in "A Walk on the Moon". In 1986, he was in "No Mercy", as a member of a socially prominent New Orleans family whose interest in Kim Basinger makes him susceptible to a gangster and was a potentially sleazy photographer in "Seven Minutes in Heaven". He was John Cameron, the friend of Hawkeye (Daniel Day-Lewis) and a settler whose family is murdered by Huron warriors and 'Les Francais' in "The Lost of the Mohicans" (1992). Kinney had one of his best chances the next year in Sydney Pollock's "The Firm", in which he was the younger partner who was supposed to look out after Tom Cruise. He starred in "The Body Snatchers" (also 1993), the updated remake of "Invasion of the Body Snatchers", and was the rich Brahmin who loves Jennifer Beals but cannot marry her in "Devil in a Blue Dress" (1995).
Kinney had an auspicious TV debut in the miniseries "Murder Ordained" (CBS, 1987), as a charismatic minister who begins an affair with JoBeth Williams and then convinces her they should each murder their spouses so they can be together. In 1993, he was Joseph Kennedy Sr. in the longform, "JFK: Reckless Youth." For two seasons (1987-89), he appeared on ABC's "thirtysomething" as the beau of Ellyn (Polly Draper) and more recently has portrayed the prison administrator on the HBO series "Oz" (1997- ).