I need to know how and why companies use air cooled blast furnace slag in the manufacture of cement.

Air-cooled blast furnace slag can be added to the inlet of the cement kiln in the patented Cemstar process developed by TXI cement in the USA. I know a number of US cement companies are doing this. This is in the manufacture of cement powder. Another use is as an aggregate in the manufacture of concrete.

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 the feed 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?