Infrared-dark clouds (IRDCs) are believed to be the birthplaces of rich clusters and thus contain the earliest phases of high-mass star formation. We use the Green Bank Telescope and Very Large Array maps of ammonia (NH3) in six IRDCs to measure their column density and temperature structure (Paper 1), and here, we investigate the kinematic structure and energy content. We find that IRDCs overall display organized velocity fields, with only localized disruptions due