One US gallon is 231 cubic inches.

One square yard is 1296 square inches.

So "1 inch of rain" is 1296/231 or about 5 and a half US gallons or 21 liters of water per square yard. 

The flow rate through your drip system obviously depends on the area it is watering and how many hours it is on each day, but that gives you a starting point.

Note: 1 imperial (UK) gallon is 277 cubic inches which gives 4 and three quarter UK gallons per square yard - but commercial UK irrigation systems will be specified in metric units so that is fairly irrelevant.