This is the second in a series of papers presenting VLBI observations of the 293 Caltech-Jodrell Bank Flat-spectrum (hereafter CJF) sources and their analysis. We obtain a consistent motion dataset large enough to allow the systematic properties of the population to be studied. We present detailed kinematic analysis of the complete flux-density limited CJF survey. We computed 2-D kinematic models based on the optimal model-fitting parameters of multi-epoch VLBA observations. This allows us to calculate not only radial, but also orthogonal motions, and thus to study curvature and acceleration. Statistical tests of the motions measured and their reliability were performed. A correlation analysis between the derived apparent motions, luminosities, spectral indices, and core dominance and the resulting consequences is described. With at least one velocity in each of the 237 sources, this sample is much larger than any available before, so it allows a meaning ful statistical investigation of apparent motions and any possible correlations with other parameters in AGN jets. The main results to emerge are as follows: * In general motions are not consistent with a single uniform velocity applicable to all components along a jet. * We find a slight trend towards a positive outward acceleration and also adduce some evidence for greater acceleration in the innermost regions. * We find a lack of fast components at physical distances less than a few pc from the reference feature. * Only ~4% of the components from galaxies and <2% of those from quasars undergo large bends i.e. within 15{deg} of +/-90{deg}. * The distribution of radial velocities shows a broad distribution of velocities (apparent velocities up to 30c). Fifteen percent of the best-sampled jet components exhibit low velocities that may need to be explained in a different manner to the fast motions. * Some negative superluminal motions are seen, and in 15 cases (6%) these are definitely significant. * We find a strong correlation between the 5 GHz luminosity and the apparent velocity. * The CJF galaxies, on average, show slower apparent jet-component velocities than the quasars. * The mean velocity in the VLBA 2cm survey (Kellermann et al. 2004) is substantially higher than in the CJF survey, the ratio could be roughly a factor of 1.5-2. This supports the observed trend toward increasing apparent velocity with in creasing observing frequency. This AGN survey provides the basis for any statistical analysis of jet and jet-component properties.