Despite many attempts ordered equilibrium microphases have yet to be obtained in experimental colloidal suspensions. The recent computation of the equilibrium phase diagram of a microscopic particle--based microphase former (Zhuang et al. Phys.~Rev.~Lett. (2016)) has nonetheless found such mesoscale assemblies to be thermodynamically stable. Here we consider their equilibrium and assembly dynamics. At intermediate densities above the order-disorder transition we identify four different dynamical regimes and the structural changes that underlie the dynamical crossovers from one disordered regime to the next. Below the order-disorder transition we also find that periodic lamellae are the most dynamically accessible of the periodic microphases. Our analysis thus offers a comprehensive view of the disordered microphase dynamics and a route to the assembly of periodic microphases in a putative well-controlled experimental system. The data files in this collection are associated with the paper "Microphase Equilibrium and Assembly Dynamics" Y. Zhang and P. Charbonneau Journal of Chemical Physics 2017. They include GLE EPS dat and png files with associated raw data and generating scripts to allow for replication of the figures.