SULAIMANIYA, Iraq—With a purple scrunchie in his pony tail, a black cap, and a platoon of blazing white teeth, Abdullah Rahman al-Shamary looks like a failed rock star. And in a way, he is. Under Saddam Hussein, al-Shamary could go anywhere and do anything. He was a “made man,” and was an officer in its feared Mukhabarat General, an intelligence service run by Saddam’s son, Qusay. And, Qusay oversaw the Mukhabarat’s relationship with Jund al-Islam, an al Qaeda wing operating in Northern Iraq before the 2003 American invasion. For the past five years, al-Shamary has languished in a prison outside...