Many instruments would fit with ist to give an answer.
If the flute is the earliest instrument it fits well with the question.
As for Americanisms in English Quizzes/Crosswords it wouldn't be the first time.
I agree that harpist is probably the required answer. Flutist doesn't quite work in my opinion since if that were the answer the first part of teh clue would be redundant. Oboeist works but I think most people would think of harpist before oboeist
I'm not aware that the setter only accept Collins. Oboeist is an alternative and in my dictionary as such. But anyway it doesn't matter because teh answer is still harpist