Two-dimensional flat-band systems have recently attracted considerable interest due to the rich physics unveiled by emergent phenomena and correlated electronic states at van Hove singularities. However, the difficulties in electrically detecting the flat-band position in field-effect structures are slowing down the investigation of their properties. In this work, we use indium selenide (InSe) as a flat-band system due to a van Hove singularity at the valence-band edge in a few-layer form of the material without the requirement of a twist angle. We investigate tunnelling photocurrents in gated few-layer InSe structures and relate them to ambipolar transport and photoluminescence measurements. We observe an appearance of a sharp change in tunnelling mechanisms due to the presence of the van Hove singularity at the flat band. We further corroborate our findings by studying tunnelling currents as a reliable probe for the flat-band position up to room temperature. Our results create an alternative approach to studying flat-band systems in heterostructures of two-dimensional materials.