Catalysis of the reaction: 2-oxoglutarate + L-kynurenine = H2O + kynurenate + L-glutamate. The product 4-(2-aminophenyl)-2,4-dioxobutanoate is converted into kynurenate by a spontaneous reaction. Also acts on 3-hydroxykynurenine to form xanthurenate.Source:EC:2.6.1.7