It has been demonstrated earlier that graphene-like defects on fluorographene can act as molecules in biomimetic molecular light-harvesting antennae. In competition with radiative and non-radiative losses, transfer time of excitations in an antenna measures its performance. We report on the optimal conditions for excitation energy transfer in artificial antennae built from selected types of fluorographene defects. The excitation transfer dynamics is calculated based on the Frenkel exciton model using hierarchical equations of motion for different values of temperature, system-environment reorganization energy and bath correlation time to study a possible range of parameters pertaining to the fluorographene material. We also study possible energy funnelling in the third dimension for two parallel fluorographene sheets with defects. We conclude that the strength of system-environment interaction is more important for the efficient energy funnelling in our proposed material than a precise control over the structure of artificial antennae.