Kenny was a patient and friend of Dr. Paul Connelly.
As Dr. Connelly was preparing him for dental surgery, Kenny admitted that he was no longer attracted to his wife because she's "too old." He then admitted that he skipped out on a camping trip with Dr. Connelly and his family because he was afraid of what he'd do to Dr. Connelly's young daughter. As Dr. Connelly became more and more agitated, Kenny blithely continues to speak, finally admitting to engaging in sexual relations with Dr. Connelly's daughter while she was at his house for his own daughter's sleepover. In a fit of rage, Dr. Connelly killed Kenny with his dentist's drill.
Sam and Dean eventually learn that Veritas, the goddess of truth, was summoned in Calumet City, and anyone who wished out loud for the truth will be bombarded with it until they die. It was likely that it was Dr. Connelly who was suffering Veritas' curse. Veritas was a pagan deity and ate human flesh, and so it is implied that Kenny was eaten by Veritas after his body disappeared from the city morgue.