We derive closed form solutions for the effective diffusion coefficient of flake-filled composites, in which the flakes are randomly placed and oriented, with their orientations uniformly distributed in an interval [-ε, +ε], 0<ε<π/2. Our solutions are based on the arithmetic and harmonic averaging of the diffusivity of unidirectional misaligned flake systems, the latter expressed in terms of the principal components of the diffusivity tensor. Using large-scale 2D simulations spanning the regime from dilute to highly concentrated, the proposed solutions are tested against and confirmed by computational results. We use both, traditional 2D and also 1D representations of the flake cross-sections. The 1D representation is suitable for very high aspect ratio flakes, such as exfoliated nano-platelets of montmorillonite or graphene-oxide. This approach greatly simplifies the construction of the computational mesh. It is also the only feasible approach to model flake nano-composites (α>1000), in which (αφ) can reach levels in excess of 100. Such high levels of (αφ) are obviously unrealistic in traditional flake composites and existing literature has reported results for values of (αφ) only up to 10. Comparison of the derived closed form solutions to computational results reveals that both the harmonic and the arithmetic averages are adequate in dilute systems; however, at large values of (αφ) and (ε) only the harmonic average is in good agreement with the computational results. The predictions of the proposed solution (harmonic averaging) are also compared to those of existing literature models for the effective diffusivity of flake composites. We find that discrepancies become very significant at large (ε) and also at large values of (αφ), pointing further to the conclusion that the proposed solution is currently the only accurate one to predict the effective diffusivity of randomly oriented and highly concentrated nano-flake composites.