Can someone explain why the electrical conductivity of magnesium chloride decreases with increasing concentration?
You simply started your data range at too high a concentration to see the initial increase.  Semantic Scholar gives data for the conductivities of several aqueous electrolyte solutions at 25°C, including magnesium chloride.  The strongly increasing portion of the magnesium chloride curve goes up to about 10%, which corresponds to about one molar (where your data happens to start).