Response to 30 Very British Problems:
Well the proper answer would be “I don’t know”. The person is asking if he is able to to get his own coffee. The barista, apart from probably being reluctant to let someone serve theirself, does not know whether the customer is actually able to operate the machine to make his own coffee. Of course in Australia, and maybe the US, “canIgetacoffee” means “mayIhaveacoffee (please)”.