Single- and few-layered InSe flakes are produced by the liquid-phase exfoliation of beta-InSe single crystals in 2-propanol, obtaining stable dispersions with a concentration as high as 0.11 g/L. Ultracentrifugation is used to tune the morphology, i.e., the lateral size and thickness of the as-produced InSe flakes. We demonstrate that the obtained InSe flakes have maximum lateral sizes ranging from 30 nm to a few um, and thicknesses ranging from 1 to 20 nm, with a max population centred at ~ 5 nm, corresponding to 4 Se-In-In-Se quaternary layers. We also show that no formation of further InSe-based compounds (such as In2Se3) or oxides occurs during the exfoliation process. The potential of these exfoliated-InSe few-layer flakes as a catalyst for hydrogen evolution reaction (HER) is tested in hybrid single-walled carbon nanotubes/InSe heterostructures. We highlight the dependence of the InSe flakes morphologies, i.e., surface area and thickness, on the HER performances achieving best efficiencies with small flakes offering predominant edge effects. Our theoretical model unveils the origin of the catalytic efficiency of InSe flakes, and correlates the catalytic activity to the Se vacancies at the edge of the flakes.