Modeling fluid flow dynamics in metal organic frameworks (MOFs) is a required step toward understanding mechanisms of their activity as novel catalysts, sensors, and filtration materials. We adapted a lattice Boltzmann model, previously used for studying flow dynamics in meso- and microporous media, to the nanoscale dimensions of the MOF pores. Using this model, rapid screening of permeability of a large number of MOF structures, in different crystallographic directions, is possible. The method was illustrated here on the example of an anisotropic MOF, for which we calculated permeability values in different flow directions. This method can be generalized to a large class of MOFs and used to design MOFs with the desired gas flow permeabilities.