Insulating films are essential in multiple electronic devices because they can provide essential functionalities, such as capacitance effects and electrical fields. Two-dimensional (2D) layered materials have superb electronic, physical, chemical, thermal, and optical properties, and they can be effectively used to provide additional performances, such as flexibility and transparency. 2D layered insulators are called to be essential in future electronic devices, but their reliability, degradation kinetics, and dielectric breakdown (BD) process are still not understood. In this work, the dielectric breakdown process of multilayer hexagonal boron nitride (h-BN) is analyzed on the nanoscale and on the device level, and the experimental results are studied via theoretical models. It is found that under electrical stress, local charge accumulation and charge trapping/detrapping are the onset mechanisms for dielectric BD formation. By means of conductive atomic force microscopy, the BD event was triggered at several locations on the surface of different dielectrics (SiO2, HfO2, Al2O3, multilayer h-BN, and monolayer h-BN); BD-induced hillocks rapidly appeared on the surface of all of them when the BD was reached, except in monolayer h-BN. The high thermal conductivity of h-BN combined with the one-atom-thick nature are genuine factors contributing to heat dissipation at the BD spot, which avoids self-accelerated and thermally driven catastrophic BD. These results point to monolayer h-BN as a sublime dielectric in terms of reliability, which may have important implications in future digital electronic devices.