Self-assembled linear chains of CdSe nanoplatelets are known to exhibit highly efficient Förster resonant energy transfer (FRET) leading to fast exciton diffusion between platelets. Here, we compare the luminescence decay dynamics of single nanoplatelets, clusters of a few platelets, and selfassembled chains. As the number of stacked platelets is increased, we show that the luminescence decay becomes faster, which can be interpreted as FRET-mediated effect of quenchers: excitons may diffuse to nearby quenchers so that their decay rate is increased. On the other hand, a minor slow decay component is also observed for single platelets, corresponding to trapping-detrapping mechanisms in nearby trap states. The contribution of the slow component is enhanced for the platelet chains. This is consistent with a FRET-mediated trapping mechanism where the excitons would diffuse from platelet to platelet until they reach a trap state. Finally, we develop toy models for the FRETmediated quenching and trapping effects on the decay curves and analyze the relevant parameters.