The feature of self-cleansing in sewer pipes is a standard requirement in the design of drainage systems, as sediments deposited on the channel bottom cause changes in channel geometric properties and in hydrodynamic parameters, including the friction caused by the cohesive forces of sediment fractions. Here, it is shown that the content of cohesive fractions significantly inhibits the transport of non-cohesive sediments. This paper presents an advanced calculation procedure for estimating flushing flows in channels. This procedure is based on innovative predictive models developed for non-cohesive and granulometrically heterogeneous sediment transport with additional cohesive fraction content to estimate the magnitude of increased flow necessary to ensure self-cleansing of channels. The computations according to the proposed procedure were carried out for a wide range of hydrodynamic conditions, two grain diameters, six cohesive (clay) fraction additive contents and two critical stress values. The trend lines of calculations were composed with the results of experimental studies in hydraulic flumes.