"It appears he just jumped in the vehicle and left," Donovan spokesman Lt. Patrick Logan said.
Kelley was in jail for a parole violation, Logan said. Kelley was at large as of Monday night.
Logan said inmates assigned to firefighting duties are screened and given a measure of freedom because they are housed outside the prison's secure perimeter.
A release from Donovan facility Monday said deputies saw a fire truck driving erratically in Spring Valley, about 10 miles from the prison. When the deputies pulled the engine over, the driver fled.