Magnetohydrodynamic (MHD) waves are regularly observed in the finely structured, highly dynamic solar atmosphere. This dynamic behavior in plasma environments gives rise to plasma flows, that can lead to the instability of waveguides. Recent studies have employed the method of introducing waveguide asymmetry to generalise ‘classical’ symmetric descriptions of the fine structuring within the solar atmosphere, with some of them introducing steady flows as well. The presentation will share our analytical investigations validated by numerical simulations on how the phase speeds of the guided waves change, and where possible, determine the limiting flow speeds required for the onset of the Kelvin-Helmholtz instability (KHI). This way we can better understand the additional physics stemming from introducing further sources of asymmetry. Specifically the presentation will delve into geometries where the magneto-acoustic waves are guided by a magnetic slab within an asymmetric magnetic environment, in which the slab is under the effect of a steady flow. Furthermore a non-parallel case will also be shared where the slab is without material flow. The new results expand on established knowledge regarding the propagating MHD waves in magnetic slabs and in the non-parallel case will bring into light new features such as modes changing character and some generalising velocities replacing Alfvén and sound speeds.