Why does chocolate burn if you microwave it with milk?

As already pointed out, microwaves in the oven have just the right frequency to heat water molecules. But this alone does not explain why chocolate with a tiny bit of milk heats up so much quicker than a glass of milk. The key is heat capacity.

With no milk the chocolate is almost transparent to the microwaves. Even a little bit of milk makes the mixture capable of absorbing a substantial portion of the energy the microwaves bring in. This energy is then spread out through the mixture of chocolate and milk. The heat capacity of the mixture is essentially that of chocolate if there is little milk, and the specific heat capacity of chocolate is much lower than that of water or milk. Therefore it takes less energy to heat chocolate to such temperatures that it burns.

If there is too little milk, you don't catch enough of the energy of the microwaves. If there is too much milk, it increases the heat capacity and slows down the heating. Somewhere in between there is a sweet spot where the milk acts as a microwave antenna for the chocolate but does not take up a substantial portion of the total heat.

I am not commenting on what the burning of the chocolate actually means. This answer only concerns the energy transfer process that leads to temperature change at different rates. The temperature around the boiling point of milk (≈water) is not enough for combustion but is enough for other processes that change the color and flavor of the chocolate. Also, sensitivity to microwave heating is not binary; plain chocolate heats up too but less so than milk, and it also depends on the variety of chocolate in use.

I'm not an expert in this field and definitely not a good cook but I think when you heat up your milk, after some point it's proteins cluster and sticks to your cup because there are imperfections in the material even if they are not visible. (that's why when people boil milk, they add small amount of water for it to serve as an insulating layer between the pan and milk) Even in case of chocolate, if you heat it up to 50°C it will burn.