  There are ubiquitous flows observed in the solar atmosphere of
sub-Alfv\'{e}nic speeds, however after flaring and coronal mass ejection events
flows can become Alfv\'{e}nic. In this Letter, we derive an expression for the
standing kink mode frequency due to siphon flow in coronal loops, valid for
both low and high speed regimes. It is found that siphon flow introduces a
linear spatially dependent phase shift along coronal loops and asymmetric
eigenfunctions. We demonstrate how this theory can be used to determine the
kink and flow speed of oscillating coronal loops with reference to an
observational case study. It is shown that the presence of siphon flow can
cause the underestimation of magnetic field strength in coronal loops using the
traditional seismological methods.
