Magnetohydrodynamic waves are ubiquitously detected in the finely structured solar atmosphere. At the same time, our Sun is a highly dynamic plasma environment, giving rise to flows of various magnitudes, which can lead to the instability of waveguides. Recent studies have employed the method of introducing waveguide asymmetry to generalize “classical” symmetric descriptions of the fine structuring within the solar atmosphere, with some of them introducing steady flows as well. Building on these recent studies, here we investigate the magnetoacoustic waves guided by a magnetic slab within an asymmetric magnetic environment, in which the slab is under the effect of a steady flow. We provide an analytical investigation of how the phase speeds of the guided waves are changed, and where possible, determine the limiting flow speeds required for the onset of the Kelvin–Helmholtz instability. Furthermore, we complement the study with initial numerical results, which allows us to demonstrate the validity of our approximations and extend the investigation to a wider parameter regime. This configuration is part of a series of studies aimed to generalize, step-by-step, well-known symmetric waveguide models and understand the additional physics stemming from introducing further sources of asymmetry.