What could be the minimum velocity of gases in downcomer duct? Our idea is to reduce velocity by increasing duct diameter, as much as possible so as to get lowest pressure drop across downcomer duct.

: I don't think there is a minimum velocity in the downcomer duct. You must draw the exhaust gases out of the kiln, but provided you do that adequately it does not matter at what velocity they flow down the downcomer duct. However, I'm not sure what you are going to achieve by this modification. The pressure drop across the downcomer duct is unlikely to be a limiting factor on your kiln. That limiting pressure drop will be elsewhere in the system.

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?