The self-assembly of amphiphilic Janus colloids in microfluidic channels is studied using hybrid molecular dynamics simulations with fully resolved hydrodynamic interactions incorporated through the multi-particle collision dynamics algorithm. The simulations are conducted at a density and temperature where the Janus particles spontaneously self-assemble into spherical micelles to minimize the interface between the solvophobic caps and the surrounding solvent. In confined systems, this contact area can also be reduced by aggregation at the channel walls. Indeed, a sizable fraction of free particles and small clusters with three and four members are found at the walls when the microfluidic channel is made up of a comparably solvophobic material as the Janus colloids. When the applied Poiseuille flow is sufficiently strong, the colloidal micelles break up into smaller fragments and isolated particles. However, at intermediate flow rates the shear-induced dissociation and reorganization of aggregates lead to a net growth of the micelles with a sizable amount of particles in icosahedral clusters with 13 particles. Furthermore, the parabolic velocity profile of the flow causes a highly non-uniform cluster size distribution between the channel walls, where the aggregation number decreases close to the walls.