How to convert rainfall rate (kg m-2 s-1) to rainfall(mm)?

Multiply the rate (given in Kg/m^2/s) by 1 to get the rainfall in terms of mm/s. Note that while your post asked for it in terms of mm, it actually converts to mm per second.

This is based on the following calculation: 1 Kg of water = 1 L volume = 1000 cm^3 volume. If you spread 1000 cm^3 over an area of 1 square meter, the water would be 0.1 cm deep, or 1 mm. Hence 1 Kg/m^2 is equivalent to 1 mm of depth.