  It is well established now that the solar atmosphere, from photosphere to the
corona and the solar wind is a highly structured medium. Satellite observations
have confirmed the presence of steady flows. Here, we investigate the parallel
propagation of magnetohydrodynamic (MHD) surface waves travelling along an
ideal incompressible flowing plasma slab surrounded by flowing plasma
environment in the framework of the Hall magnetohydrodynamics. The propagation
properties of the waves are studied in a reference frame moving with the mass
flow outside the slab. In general, flows change the waves' phase velocities
compared to their magnitudes in a static MHD plasma slab and the Hall effect
limits the range of waves' propagation. On the other hand, when the relative
Alfvenic Mach number is negative, the flow extends the waves propagation range
beyond that limit (owing to the Hall effect) and can cause the triggering of
the Kelvin--Helmholtz instability whose onset begins at specific critical wave
numbers. It turns out that the interval of Alfvenic Mach numbers for which the
surface modes are unstable critically depends on the ratio between mass
densities outside and inside the flux tube.
