Which of the following solids is the best insulator: magnesium, iron, gold, or magnesium fluoride?

To answer this question, we need to compare the conductivity of each material.

It's not clear whether you meant thermal or electrical conductivity, but the two are strongly correlated and the answer is the same either way: Magnesium fluoride.

Electrical conductivity of magnesium fluoride is negligible in solid state, while for gold it is` 4.10*10^7 S/m` , for iron it is `1.00*10^7 S/m` , and for pure magnesium it is `2.24*10^7 S/m` . So magnesium fluoride is the best electrical insulator by far.

As for thermal conductivity, magnesium fluoride is `14.5 W/(mK)` , while for gold it is `315 W/(mK)` , iron `73 W/(mK)` , and for pure magnesium it is `159 W/(mK)` . Magnesium fluoride is also the best thermal insulator.