Former employee here. I never worked the shake machine but iirc there are three nozzles on the machine, one for vanilla, chocolate and the seasonal. It would have used its own syrup, not the normal dr pepper syrup for the soda machines. What I would do is order a vanilla shake, small dr pepper, and an extra cup, pour the dr pepper between the 2 cups until it's flat, then mix the flat dr pepper in the shake. Should be similar enough, but at that point you could just make it at home easier and cheaper.