We present kinematic analyses of the 12 galaxies in the "Survey of H i in Extremely Low-mass Dwarfs" (SHIELD). We use multi-configuration interferometric observations of the H i 21 cm emission line from the Karl G. Jansky Very Large Array (VLA)22 to produce image cubes at a variety of spatial and spectral resolutions. Both two- and three-dimensional fitting techniques are employed in an attempt to derive inclination-corrected rotation curves for each galaxy. In most cases, the comparable magnitudes of velocity dispersion and projected rotation result in degeneracies that prohibit unambiguous circular velocity solutions. We thus make spatially resolved position-velocity cuts, corrected for inclination using the stellar components, to estimate the circular rotation velocities. We find 30 km s-1 for the entire survey population. Baryonic masses are calculated using single-dish H i fluxes from Arecibo and stellar masses derived from HST and Spitzer imaging. Comparison is made with total dynamical masses estimated from the position-velocity analysis. The SHIELD galaxies are then placed on the baryonic Tully-Fisher relation. There exists an empirical threshold rotational velocity, V < 15 km s-1, below which current observations cannot differentiate coherent rotation from pressure support. The SHIELD galaxies are representative of an important population of galaxies whose properties cannot be described by current models of rotationally dominated galaxy dynamics.