The rate of bedrock channel incision is key to the understanding of landscape evolution. Theoretical models relate channel incision to sediment transport; the latter conditioned by the bed shear stress. However, theory is deficient in an appreciation of the transverse and vertical flow structure that mediates shear stress for deep, narrow inner‐channels, which often characterize large bedrock rivers. Here we present the detail of the structure of high Reynolds number flows for bedrock‐controlled rapids of the Mekong River, SE Asia. Distinct filaments of high‐velocity flow, separated by regions of slower flow, occur across channels; the numbers of filaments scale linearly with channel width to maximum‐depth (B/hmax) ratios. Inner‐channels with low ratios (B/hmax < 20) exhibit wall‐effected flow structure. Effects include suppressed maximum velocity filaments due to: (i) significant channel‐transverse flow; (ii) strongly‐sheared vertical flow structure; and (iii) significant underflows. Such complex water column flow patterns largely defy theoretical description. Nonetheless near the bed, the vertical velocity distributions often conform to: (i) ‘law‐of‐the‐wall’ logarithmic theory; or (ii) profiles in the near‐bed region and within the transition to outer flow can be described using a log‐wake function. Consequently, for selected velocity profiles it is possible to derive hydraulic parameters suitable for input to incision models. Chezy‐C values are high, indicating low flow resistance, while bed shear stresses remain competent, even during low‐discharges, to transport cobble bedload across low roughness bedrock surfaces. Thus, as competence is high, no blanketing sediment deposits can develop within inner channels to prevent bedrock erosion. Consequently, within similar high competence systems, incision is probably progressive as long as sediment supply is sustained to abrade the bedrock. The landscape modelling implication is that abrasion in this system is supply‐limited and not limited by flow competence. In contrast, a transport‐limited system is likely to evolve to exhibit an alluvial bed. © 2018 John Wiley & Sons, Ltd.