Peptide-appended Pillararene (PAP) is an artificial water channel that can be incorporated into lipid and polymeric membranes to achieve high permeability and enhanced selectivity for angstrom-scale separations [Shen et al. Nat. Commun. 9:2294 (2018)]. In comparison to commonly studied rigid carbon nanotubes, PAP channels are conformationally flexible, yet these channels allow a high water permeability [Y. Liu and H. Vashisth Phys. Chem. Chem. Phys. 21:22711 (2019)]. Using molecular dynamics (MD) simulations, we study water dynamics in PAP channels embedded in biological (lipid) and biomimetic (block-copolymer) membranes to probe the effect of the membrane environment on water transport characteristics of PAP channels. We have resolved the free energy surface and local minima for water diffusion within the channel in each type of membrane. We find that water follows single file transport with low free-energy barriers in regions surroundings the central ring of the PAP channel and the single file diffusivity of water correlates with the number of hydrogen bonding sites within the channel, as is known for other sub-nm pore-size synthetic and biological water channels [Horner et al. Sci. Adv. 1:e1400083 (2015)].