Wind chill works by removing the layer of heated air around your body. However in a hot area, say a desert, wouldn't the air around be hotter than your body or at least much closer to it than cold air? In that case, how much would wind chill actually affect your temperature loss?
As you state, wind chill "is the cooling of a body due to the passing-flow of lower temperature air.
Because of this, wind chill only occurs when then air had capacity to absorb heat from a body - thus chilling the body. The capacity of air to absorb heat from a body is dependent on the temperature difference between the air and the body, and the humidity of the air.
In determining the ability of the air to absorb heat , the wet bulb temperature must be used, in conjunction with the dry bulb. Wind chill and [heat index] (https://en.wikipedia.org/wiki/Heat_index) are related.
In a hot environment, such as a very hot day in a desert, a wind chill factor usually will usually not exist. Under such conditions is it possible to a body to over heat and experience heat stress and hyperthermia, which can lead to death. Also, one has to be careful so that wind burn doesn't occur.