Kenrick was born in Astoria, New York.

In the 1980s and 1990s, Kenrick pursued a career in theatrical production and management. Productions on which he worked included the 1994 Broadway revival of Grease and the original 1996 Broadway production of Rent, as well as national tours of Damn Yankees, Crazy for You, Victor/Victoria, Jekyll & Hyde, and the original 1995 touring production of Busker Alley. He wrote the lyrics for the Off-Broadway musical Bats and has written material for various cabaret and comedy acts. He served as Associate Producer for the Celebration '86 Gay Arts Festival.

Kenrick teaches musical theatre history at New York University's Steinhardt School and has also taught the subject at Marymount Manhattan College. He is a frequent lecurer on theatre and film history. Broadway World calls him an "Internationally recognized musical theatre and film authority". He is often cited as an expert in the press. Kenrick has been interviewed about theatre and film on numerous U.S. and UK television and radio programs and in national and foreign newspapers and magazines. He has been interviewed in documentaries concerning showtunes, Jerry Herman, Times Square, haunted theatres, and the history of burlesque, and he appears in the DVD documentaries for The Busby Berkeley Collection and for the film musicals Three Little Words, Till the Clouds Roll By and It's Always Fair Weather. Among other lecture series, from 2005 to 2007, he gave a three-year "musical conversation" series at York Theatre Company. Kenrick has appeared in several documentaries about musicals.

Kenrick is the curator of the extensive musical theatre and film website Musicals101.com: The Cyber Encyclopedia of Musical Theatre, TV and Film. Hundreds of libraries, universities and arts sites link to Musicals101.com.