We propose and compare different strategies to construct dynamic density functional theories (DDFTs) for inhomogeneous polymer systems close to equilibrium from microscopic simulation trajectories. We focus on the systematic construction of the mobility coefficient, Lambda(r,r'), which relates the thermodynamic driving force on monomers at position r' to the motion of monomers at position r. A first approach based on the Green-Kubo formalism turns out to be impractical because of a severe plateau problem. Instead, we propose to extract the mobility coefficient from an effective characteristic relaxation time of the single chain dynamic structure factor. To test our approach, we study the kinetics of ordering and disordering in diblock copolymer melts. The DDFT results are in very good agreement with the data from corresponding fine-grained simulations.