Velocity dispersion profiles and rotation curves have been determined for a sample of 13 brightest duster galaxies (BCGs) in order to study their internal stellar kinematics and investigate their relationship to ellipticals. We find that BCGs generally display velocity dispersion profiles with gradients similar to those found in normal bright ellipticals. A rising velocity dispersion profile is found for the BCG IC 1101, the dominant member of Abell 2029, confirming Dressier's (1979) result. No other rising velocity dispersion profiles are found in our sample suggesting that they are not a feature common to brightest duster galaxies. Significant rotation is found in only two of the galaxies, a result in agreement with previous studies showing the declining importance of rotation with increasing luminosity for elliptical galaxies. Our data suggest that environment plays a role in the kinematic characteristics of BCGs. We find a correlation between the rotation of BCGs and the velocity dispersion of their parent clusters in the sense that very slowly rotating galaxies (V-m/(sigma))(not asymptotic to) 650 km s(-1)) clusters. This relation between the internal stellar kinematics of BCGs and the cluster velocity dispersion is in the sense expected if ellipticals formed by merging. Brightest duster galaxy mass-to-light ratios derived from photometric and kinematic modeling are found to be similar to normal elliptical M/L values. For the galaxy NGC 4073, the dominant galaxy in the poor cluster MKW 4, we find that it contains a counterrotating stellar core suggestive of the occurrence of an accretion event(s).