What are the characteristics required for a liquid be considered milk?
It has to remind people of milk in looks and consistency and not be too strongly flavored of something else. 

Really, there is no authority which appoints stuff as "milk". If it looks sufficiently like milk, it is likely that people will call it milk. If it is edible and available in large quantities (unlike the milk of, say, Euphorbia) people will try using it as milk - drinking it pure, adding it to coffee, making crepes with it, etc and thinking of it as just another kind of milk. 

If you are unhappy with this answer because it doesn't list an objective decision criterion for dividing stuff into "milk" and "not milk", you need to realize that we are not dealing with mathematical sets here, but with cultural categories. Cultural categories are ill-defined, and membership in one is determined primarily by perceived similarities to the prototypical member of the category, in this case visual similarity to cow's milk.