The conduction cooling HTS SMES magnet is operated in cryogenic temperature. The insulation design at cryogenic temperature is an important element that should be established to accomplish miniaturization that is a big advantage of HTS SMES. However, the behaviors of insulators for cryogenic conditions in air or vacuum are virtually unknown. Therefore, we need active research and development of insulation concerning application of the conduction cooling HTS SMES. Specially, this paper was studied about high vacuum and cryogenic temperature breakdown and flashover discharge characteristics between cryocooler and magnet-coil. The breakdown and surface flashover discharge characteristics were experimented at cryogenic temperature and vacuum. Also, we were experimented about mechanical properties of 4-point bending test. From the results, we confirmed that about research between cryocooler and magnet-coil established basic data in the insulation design.