The production of transparent wood is based on delignification of wood followed by infiltration of a suitable polymer. The infiltration behavior of the delignified wood scaffold is based on its permeability -- hence, predicting the permeability across hierarchical length scales is essential for process optimization. Wood exhibits a highly complex multiscale structure, spanning from nanoscale cellulose assemblies and submicron pore networks to macroscopically anisotropic growth-ring patterns. Delignification alters this structure substantially by removing lignin, modifying pore connectivity, and increasing accessible void volume, which governs how polymer precursors can permeate the scaffold. We present a multiscale modeling framework allowing for permeability upscaling of delignified wood, providing a predictive alternative to extensive experimental characterization for each wood-polymer combination. Building on continuum micromechanics-based homogenization, the approach integrates structural information across multiple observation scales. The model enables estimation of permeability tensors that reflect both the anisotropy and the hierarchical porosity of the treated wood. First, the model is experimentally validated based on comparing model predictions with pertinent experimental data available in literature. Then, permeability upscaling is applied to (i) pristine wood, allowing for experimental validation through comparison with pertinent experimental data; (ii) delignified wood, for assessment of the aforementioned infiltration behavior; and (iii) also to transparent wood, to quantify the extent of permeability reduction upon occupation of the large pore spaces of wood by a polymer. The results provide unprecedented insights concerning the polymer infiltration behavior, thereby supporting the rational design of transparent-wood fabrication processes.