Conductivity depends primarily on three factors: (i) concentration of ions, (ii) Temperature (iii) type of substance.

In our case, temperature is assumed to be same. This leaves the deciding factor as the cations of both substances (since both have chloride ions)

${\mathrm{K}}^{+}$ will have higher conductivity than $\mathrm{N}{\mathrm{a}}^{+}$ since the degree of hydration for $\mathrm{N}{\mathrm{a}}^{+}$ is greater which reduces its mobility.

Hence, $\mathrm{K}\mathrm{C}\mathrm{l}$ having higher conductivity.