For two electrode system, through simulation if I know the concentration of ions (K+ and OH-) at the electrode, is it possible to calculate dielectric constant of the EDL?
The double layer formation is the interfacial phenomenon and you must also know about the surface charge at the electrode surface. The solution concentration information is not enough to get the estimation of double layer capacitance and/or dielectric constant. Also, it is very important to know about structure of double layer i.e. inner and outer layer thickness and corresponding electric field therein etc. Theoretically, the dielectric constant of EDL may be different from the experimental value due to specific adsorption/desorption of ionic species which are influenced by the electrode surface morphology, texture, defects and inhomogeneities in the microstructure etc. Do not forget the hydrodynamics (i.e. electrolyte stirring), which greatly affect the EDL structure as well. Also there are good research paper which describe these issues, there is one as mentioned by Dr. Alaa Faid.