We study the displacement flow of two Newtonian fluids in an inclined two-dimensional channel. The fluids have the same viscosity but different densities. The displacing fluid is denser than the displaced fluid and the flow direction is density-unstable. Three dimensionless groups largely describe these flows: the densimetric Froude number (Fr), the Reynolds number (Re) and the duct inclination (β). As a first order approximation, we are able to classify different flow regimes phenomenologically in a two-dimensional (Fr; Re cos β/Fr)-plane and provide leading order expressions for the transitions between different regimes. The effect of the imposed flow on macroscopic diffusion is also investigated for the mixing flows. The stabilizing and/or de-stabilizing effects of the imposed mean flow on buoyant exchange flows (zero imposed velocity) are described for a broad range of dimensionless parameters. It is concluded that although qualitative similarities exist, the underlying phenomena and flow regimes can be quite different for pipe and two- dimensional channel geometries. The channel flow displacement seems to destabilize more than the pipe flows. Another key difference between channel and pipe flow displacements is that the slumping pattern is more pronounced in the latter.