The optical conductivity of BaCoS₂ shows an unusual linear frequency dependence, over a broad spectral range, in contradiction with a Mott charge-transfer insulator scenario assumed for this material. A linear optical conductivity is generally explained by the presence of Dirac-cones in three dimensions. However, the Dirac cones in BaCoS₂ are far from the Fermi level. An ab initio DMFT calculation, including a retarded Hubbard interaction, explains the data in terms of an incipient opening of a Co(3d)-S(3p) charge-transfer gap together with an incoherent charge transport driven by electronic correlations. We show that BaCoS2 does not follow a Fermi liquid scenario and has Hund's metal properties arising from an incipient Mott phase destabilized by strong low-energy charge fluctuations.