The electronic anomalous Hall effect (AHE), where charge carriers acquire a velocity component orthogonal to an applied electric field, is one of the most fundamental and widely studied phenomena in physics. There are several different AHE mechanisms known falling into intrinsic and extrinsic regimes. The skew scattering mechanism (extrinsic) applies to high conductivity materials and has traditionally focused on ferromagnetic metals. Here we report the observation of a giant extrinsic AHE in KV₃Sb₅, an exfoliable Dirac semimetal with a spin 1/2 Kagome layer of Vanadium atoms. Our exfoliated flake devices reach low resistivity ~1.6 μΩ cm at low temperature and even though KV₃Sb₅ shows no magnetic ordering down to 0.25 K, the anomalous Hall conductivity (AHC) reaches ~10000 Ω^-1cm^-1 with a skew constant of 0.013, nearly an order of magnitude larger than Fe. Surprisingly, the AHE scales with the square of the longitudinal conductivity, defying expectations from skew scattering theory. This observation invites a wider variety of materials to be investigated for giant anomalous AHE including metallic magnetically frustrated materials and cluster magnets as well as posing new fundamental questions about high conductivity AHE mechanisms.