Kunken was raised on Long Island in Upper Brookville, New York. His father is a dentist and his mother is a former grade school Teacher. Kunken received a B.A. degree from Tufts University in 1993. He is a graduate of the Juilliard School's Graduate Acting program, where as a member of the Drama Division's Group 26 (1993–1997) he was awarded both The John Houseman Prize and the Pearl and Rolands Grant. His classmates included David Denman and Alan Tudyk.
He performed in The Story (2003), Henry VIII (1997) and A Dybbuk (1997) at the Public Theater..
He played the title role as Nikolai Nabakov in Lincoln Center Theater's production of Richard Nelson's Nikolai and the Others in 2013. He has appeared as Dr. Phil in the critically acclaimed production of Kate Fodor's romantic comedy RX (2012, Primary Stages production); as the Stage Manager in the 2009 David Cromer-directed revival of Thornton Wilder's Our Town (replacement as of January 5, 2010, Barrow Street Theatre); Theresa Rebeck's Our House (2009, Playwrights Horizons); Fabulation at Playwrights Horizons (2004); A Very Common Procedure by Courtney Baron at Manhattan Class Company (2007) (for which he received a Drama League Award nomination); Journals of Mihail Sebastian by David Auburn with the Keen Company in 2004 and Misalliance at the Roundabout Theatre Company (1997).
Kunken has appeared on Broadway as David Halberstam in David Auburn's The Columnist (2012); opposite Kathleen Turner in High (2011); Tom Stoppard’s Rock 'n' Roll (2007); Frost/Nixon (2007) (for which he received Outer Critics Circle Award (Outstanding Featured Actor in a Play) and Drama League Award nominations), ; Festen (2006); and Proof (replacement, 2002). For his role as CFO Andrew Fastow in Lucy Prebble's Enron, he received a 2010 Tony Award nomination for Featured Actor in a Play.
In film, Kunken's work includes The Wolf of Wall Street (2013), Still Alice (2014), Cafe Society (2016), A Birder's Guide to Everything (2014), The Bay (2012), Price Check (2012), Extremely Loud and Incredibly Close (2011), All Good Things (2010), Taking Woodstock (2009), The Girl in the Park (2008), Wait 'til This Year, Light and the Sufferer (2014), and Bamboozled (2000).
Regionally, Kunken has appeared in Quartermaine’s Terms (2009), True West (2009), Three Sisters as Solyony (2008) all at the Williamstown Theatre Festival; and Mister Roberts as Doc at the Kennedy Center in 2005, among many other credits.
