A flexible display encapsulation layer may be used to encapsulate and protect organic light-emitting diodes and a thin-film transistor layer on a flexible display. The flexible encapsulation layer may include a lateral dispersion layer that exhibits an anisotropic moisture diffusion characteristic. Lateral diffusion in the lateral dispersion layer is larger than vertical dispersion in a direction that runs perpendicular to the display. An inorganic conformal coating layer may cover the lateral diffusion layer and may serve as a pinhole filling layer. The pinhole filling layer may be covered with a moisture barrier layer that serves to prevent moisture from penetrating the display. A polymer protective layer may cover the moisture barrier layer and may be relatively insensitive to bending induced stress as the display is flexed.