Is there a formula for determining the correlation between kiln feed rate and kiln speed?

No, there is no precise formula for the relationship between kiln speed and feed rate. This depends on the degree of preparation (calcination) of thefeed at the kiln inlet and the progression of this feed preparation along the kiln length. However, there are "rules of thumb" and guidelines you can use for various kiln process types. What type of kiln are you operating?

I have two questions: What is the effect of NO_x and SO_x in controlling the burning zone temperature and what other parameters like kiln torque, kiln inlet oxygen or if anything else affects the kiln operation.
Secondly, how to improve the ventilation in ball mills, as we observe the coating formation on the balls is on the high side.

NO_x and kiln torque are both good indicators of the temperature in the burning zone of the kiln. This is key to ensuring stable operation and good combination of the clinker. Kiln inlet oxygen is a good indicator of the combustion conditions in the kiln where a small excess of oxygen is necessary to ensure burning in oxidising conditions. SO_x rises if there is reductive burning and CO present in the burning zone therefore this reinforces the kiln inlet oxygen measurement.
To improve the ventilation in the ball mill you need to increase the speed of the induced draft fan. However if you are suffering coating of the media this is more likely related to temperature control in the mill. This is a function of the clinker temperature, ventilation and the cooling with water injection.