The thermal conductivities of molten alkali fluorides (LiF, NaF, and KF) and their mixtures (LiF-NaF, LiF-KF, and NaF-KF binaries and LiF-NaF-KF ternary) are predicted using molecular dynamics simulation with the Green-Kubo method. A polarizable ion model is used to describe the interionic interactions. All the systems except LiF-KF and LiF-NaF-KF mixtures follow a scaling law: it is proportionnal to mA (-1/2)(N/V)(2/3), where mA is the arithmetic average of the ionic species masses in a given melt and N is the total number of ions included in the system volume V. In LiF-KF and LiF-NaF-KF mixtures a significant departure from the scaling law is observed. By examining separately the effects of the cation mass and size asymmetry in LiF-KF mixtures, we show that both of them account for half of the deviation. Finally, we observe that the temperature dependence of the thermal conductivity is very small in these molten fluorides.