When plates are in series, the equivalent thermal resistance is the sum of individual resistances. For equal thickness L, $R_{eq} = R_1+R_2 Rightarrow \frac{2L}{K_{eq}A} = \frac{L}{K_1 A} + \frac{L}{K_2 A}$. This simplifies to $K_{eq} = \frac{2K_1 K_2}{K_1+K_2}$.