When a firm increases all the factors of production by a factor and output increases by an equal factor. As a result the average cost for the firm stays constant.
Below is an illustration of how a business would achieve constant returns to scale. Assuming this firm only uses capital and labour as its inputs. A doubiling of the capital and labour input leads to a doubling of output as well. Because the average cost is calculated by the total costs/output, if the costs are increasing proportionately with output, average costs do not change.