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Shear viscosity is an important characterization of how a many-body system behaves like a fluid. Here we study the shear viscosity of a strongly interacting solvable model in two spatial dimensions, consisting of coupled Sachdev-Ye-Kitaev (SYK) islands. As the temperature is lowered, the model exhibits a crossover from an incoherent metal with local criticality to a marginal Fermi liquid. We find that while the shear viscosity to entropy density ratio satisfies the Kovtun-Son-Starinets (KSS) bound in the marginal Fermi liquid regime, it can strongly violate the KSS bound within a finite and robust temperature range in the incoherent metal regime, implying nearly perfect fluidity of the incoherent metal with local criticality. To the best of our knowledge, it provides the first translationally invariant example violating the KSS bound with known gauge-gravity correspondence.