The tunneling mode of scanning electrochemical microscopy (SECM) was developed recently and applied to studies of charge-transfer reactions at single metal nanoparticles (NPs). When an SECM tip is brought within the tunneling distance from a conductive NP, the particle begins to act as a part of the nanoelectrode. Herein, we demonstrate the possibility of using carbon nanoelectrodes with a very thin insulating sheath for electrochemical tunneling experiments at flat samples. In this way, electrocatalytic activity, conductivity, and charging properties of and faradaic processes in layered nanomaterials can be characterized by single-nanoflake voltammetry without making direct ohmic contact with them. A broad applicability of tunneling SECM experiments is demonstrated by probing nanomaterials with different size, geometry, and electrocatalytic properties, including metallic/pseudo-metallic (1T/1T′) and semiconducting (2H) MoS 2 nanoflakes, N-doped porous carbon catalyst, and MXene nanosheets. The Tafel plots for the hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) at individual nanoflakes are compared to analogous measurements for an ensemble of flakes attached to the surface of a macroscopic electrode. Moreover, we observed variations in catalytic activities of individual MXene flakes toward HER and OER caused by non-uniform doping.