Layered polymeric systems are widely used in membrane separation applications; chain mobility in these layered systems is a key consideration in the design of the membranes. The transport properties of membrane polymers can be significantly altered by the perturbations in chain dynamics induced by the presence of an interface and also by the topological properties of the polymers constituting the layered systems. In this work, we use molecular dynamics (MD) simulations to determine the effects of polymer backbone flexibility and interlayer interactions on the glass transition and chain dynamics of polymer layers in the layered systems. We observed that the onset of glass transition of the entire layered system is governed by the stiffer polymer layer and is independent of the type of interactions between the layers. However, the interlayer interactions govern the strength of the glass transition of the entire layered system. Polymer mobility, on the other hand, exhibits a strong dependence on both the chain flexibility and the interlayer interactions. In systems with attractive interactions between the layers, the fully flexible polymer chains at the interface have a lower mobility than those in the bulk region of the layer; the behavior differs from that of rigid polymers, which have a higher mobility at the interface compared to that in the bulk. On the other hand, when the interactions between the layers are repulsive, each layer acts as a free-standing film with chains in both the layers exhibiting higher mobility at the interface.