No, only one comma is sufficient.
What kind of music do you like? Rap,reggae or classical?
There are 2 questions here.When giving an option you use 'or' not ' and'
If you are answering the question,then it would be-
What kind of music do you like?
I like rap, reggae and classic Here, you have 3 likes,and you use the verb 'like' not 'prefer' in the answer
