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Calculating viscosity in multicompoinent metallic melts is a challenging task for both classical and \textit{ab~initio} molecular dynamics simulations methods. The former may not to provide enough accuracy and the latter is too resources demanding. Machine learning potentials provide optimal balance between accuracy and computational efficiency and so seem very promising to solve this problem. Here we address simulating kinematic viscosity in ternary Al-Cu-Ni melts with using deep neural network potentials (DP) as implemented in the DeePMD-kit. We calculate both concentration and temperature dependencies of kinematic viscosity in Al-Cu-Ni and conclude that the developed potential allows one to simulate viscosity with high accuracy; the deviation from experimental data does not exceed 9\% and is close to the uncertainty interval of experimental data. More importantly, our simulations reproduce minimum on concentration dependency of the viscosity at the eutectic point. Thus, we conclude that DP-based MD simulations is highly promising way to calculate viscosity in multicomponent metallic melts.