Debris flows are a typical hazard on steep slopes after wildfire, but unlike debris flows that mobilize from landslides, most post-wildfire debris flows are generated from water runoff. The majority of existing debris-flow modeling has focused on landslide-triggered debris flows. In this study we explore the potential for using process-based rainfall-runoff models to simulate the timing of water flow and runoff-generated debris flows in recently burned areas. Two different spatially distributed hydrologic models with differing levels of complexity were used: the full shallow water equations and the kinematic wave approximation. Model parameter values were calibrated in two different watersheds, spanning two orders of magnitude in drainage area. These watersheds were affected by the 2009 Station Fire in the San Gabriel Mountains, CA, USA. Input data for the numerical models were constrained by time series of soil moisture, flow stage, and rainfall collected at field sites, as well as high-resolution lidar-derived digital elevation models. The calibrated parameters were used to model a third watershed in the burn area, and the results show a good match with observed timing of flow peaks. The calibrated roughness parameter (Manning's $n$) was generally higher when using the kinematic wave approximation relative to the shallow water equations, and decreased with increasing spatial scale. The calibrated effective watershed hydraulic conductivity was low for both models, even for storms occurring several months after the fire, suggesting that wildfire-induced changes to soil-water infiltration were retained throughout that time. Overall the two model simulations were quite similar suggesting that a kinematic wave model, which is simpler and more computationally efficient, is a suitable approach for predicting flood and debris flow timing in steep, burned watersheds.