  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 Ly\alpha\ profiles to show that the Si II equivalent
width scales with the Ly\alpha\ 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 Ly\alpha\ escape. [abridged]
