We present an experimental study of two-dimensional dense inclined chute flows consisting of both monodisperse and bidisperse disks. We analyzed the trajectories of the particles within the flow in a steady regime. (i) In monodisperse flows, particles are arranged in layers that are in motion relative to one another, and it is found that the particles have a nonzero probability of being transferred to adjacent layers. We measured the mean time spent by a particle in a given layer. This residence time is found to decrease with increasing layer height. The particle transfer between layers can be interpreted as transverse motion of a diffusive nature. The diffusion coefficient associated with each layer increases linearly with the layer height. (ii) In polydisperse flows consisting of a small percentage (less than 1%) of small disks among large ones, the small particles have a net downward motion on which a fluctuating behavior is superimposed. At short times, the small particle motion can be described as a biased Brownian motion. The ratio of the characteristic time of diffusion to that of convection is found to increase with the layer height, indicating that the segregation process is more efficient in the upper layers of the flow. At longer times, the transverse motion of the small particles seems to differ greatly from a classical biased Brownian motion.