Manning formula is not adequate for modelling the flow resistance of a debris flow (propagation and stop), since its behaviour is not newtonian. However Manning like formula can be used for modelling the propagation of the debris flow in some situation. In an USGS Report (Water-Resources Investigations Report 85-4004 - 1985) it is reported "Roughness coefficients and hydraulic computations may not be applicable for sediment-laden flows, including mudflows and debris flows, on streams with slopes greater than 0.05, and in scoured reaches".
However if Manning formula is applied, the Manning coefficient value can be higher and higher than the case of pure water (the Manning coefficient is just a "trick" for representing the resistance), and then values of 0.05 - 0.1 or higher are not strange.
The Manning and Chezy formulae are applied only to one-dimensional, straight fixed boundary of clear water or low sediment-laden flow. So far, I have not read an article that uses Manning's classic formula to estimate debris flow velocity. If you have an article on this subject, please kindly share it.
Based on the results of large-scale flume experiments, back-calculation using superelevation may presently be the most accurate way to estimate debris flow velocity (Iverson et al. 1994). The most commonly referenced method for making this estimation is the forced vortex equation (Chow 1959; Henderson 1966; Hungr et al. 1984; Johnson 1984), which equates fluid pressure to centrifugal force (McClung 2001). Other methods may be applied, as two-phase fluid model…Several flow equations exist that can be used to predict a debris flow velocity; many of these equations are presented by Lo (2000), Rickenmann (1999), and Rickenmann and Koch (1997).