Do you have an idea of each point decreased in the standard deviation of the kiln feed and how it affects to the specific heat consumption? (for example:40 kj/kg of clinker for every additional 0.1 by which the standard deviation is raised in the usual range).

The effect of kiln feed standard deviation on unit energy consumption is complex and is likely to vary from kiln to kiln. For a precalciner kiln each one per cent increase in the standard deviation of the kiln feed lime saturation factor you might expect an increase in the energy consumption by 150 kJ/kg clinker. However, this relationship is unlikely to be linear and will vary around that figure from kiln to kiln.

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?