What are the different ways permeability of a core specimen can be determined accurately for fluids with different viscosities and their mixtures?
Strictly defined, permeability is an intrinsic property of a rock or soil, and is thus independent of the viscosity of the gas or liquid that is flowing through. Hydraulic conductivity is the equivalent measure that takes into account viscosity and fluid density. So if you have measured permeability you can calculate hydraulic conductivity for, in concept at least, any liquid.
Laboratory measurements of permeability involve passing a gas or fluid through a sample and measuring the pressure drop across the sample and the rate of flow. The characteristics of the gas or fluid are used to back calculate permeability from the measured hydraulic conductivity. Gas or fluid characteristics do influence testing - and a range of empirical corrections would be applied to account for these) (https://petrowiki.spe.org/Corrections_to_core_measurements_of_permeability)