To reionize the early universe, high-energy photons must escape the galaxies that produce them. It has been suggested that stellar feedback drives galactic outflows out of star-forming regions, creating low density channels through which ionizing photons escape into the inter-galactic medium. We compare the galactic outflow properties of confirmed Lyman continuum (LyC) leaking galaxies to a control sample of nearby star-forming galaxies to explore whether the outflows from leakers are extreme as compared to the control sample. We use data from the Cosmic Origins Spectrograph on the Hubble Space Telescope to measure the equivalent widths and velocities of Si II and Si III absorption lines, tracing neutral and ionized galactic outflows. We find that the Si II and Si III equivalent widths of the LyC leakers reside on the low-end of the trend established by the control sample. The leakers velocities are not statistically different than the control sample, but their absorption line profiles have a different asymmetry: their central velocities are closer to their maximum velocities. The outflow kinematics and equivalent widths are consistent with the scaling relations between outflow properties and host galaxy properties -- most notably metallicity -- defined by the control sample. Additionally, we use the Lyalpha profiles to show that the Si II equivalent width scales with the Lyalpha peak velocity separation. We determine that the low equivalent widths of the leakers are likely driven by low metallicities and low H I column densities, consistent with a density-bounded ionization region, although we cannot rule out significant variations in covering fraction. While we do not find that the LyC leakers have extreme outflow velocities, the low maximum-to-central velocity ratios demonstrate the importance of the acceleration and density profiles for LyC and Lyalpha escape. [abridged]
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