Active colloidal systems with non-equilibrium self-organization is a long-standing, challenging area in biology. To understand how hydrodynamic flow may be used to actively control self-assembly of Janus particles (JPs), we use a model recently developed for the many-body hydrodynamics of amphiphilic JPs suspended in a viscous background flow (JFM, 941, 2022). We investigate how various morphologies arise from tuning the hydrophobic distribution of the JP-solvent interface. We find JPs assembled into uni-lamella, multi-lamella and striated structures. To introduce dynamics, we include a linear shear flow and a steady Taylor-Green mixing flow, and measure the collective dynamics of JP particles in terms of their (a) free energy from the hydrophobic interactions between the JPs, (b) order parameter for the ordering of JPs in terms of alignment of their directors, and (c) strain parameter that captures the deformation in the assembly.We characterize the effective material properties of the JP structures and find that the uni-lamellar structures increases orientation order under shear flow, the multilamellar structure behaves as a shear thinning fluid, and the striated structure possesses a yield stress. These numerical results provide insights into dynamic control of non-equilibrium active biological systems with similar self-organization.