<p>The study investigates the linear instability of multi-diffusive convection in a horizontal Darcy–Brinkman porous layer saturated with a zero-order Kelvin–Voigt fluid (Navier–Stokes–Voigt fluid), heated and salted from below, under the framework of the local thermal non-equilibrium (LTNE) model. The momentum transfer is modelled by adopting a modified Darcy–Brinkman model, thus including the viscoelastic and viscous diffusion contributions. The stress-free boundaries are assumed to be perfect conductors of heat and solute concentrations. The stability eigenvalue problem is solved using normal-mode analysis procedure, and the onset conditions for both stationary and oscillatory convection are determined in a closed form. It is found that, in some cases, three values of the thermal Darcy–Rayleigh number are required to specify the linear instability criteria owing to the existence of disconnected closed convex oscillatory neutral curves from the stationary one. The sensitivity of the Kelvin–Voigt viscoelastic parameter on the topology of the neutral curves is examined, while its influence on the critical parameters exhibits a mixed trend—either stabilizing or destabilizing depending on the relative strength of the solutal buoyancy forces. Increased interphase heat exchange delays oscillatory convection, with both the critical thermal Darcy–Rayleigh number and the oscillation frequency approaching different limits at its asymptotic extremes. The convection cell size remains invariant at the asymptotic limits of the interphase heat transfer coefficient for all viscoelastic and Darcy numbers.</p>