First of all, thanks for posting this. I've been hearing this song on the radio, but didn't know what it was called or who sang it.
To answer your question, yes it's a natural expression. You'll hear other similar variation using 'go make yourself/myself (some) X.' Using the reflexive pronoun just sort of emphasizes the fact that the person in question is responsible for making the desired action happen.
'go make myself some money'
'go make yourself a drink'
'go make ourselves some food'
Edit: Note that at about 0:59 , he recalls his dad saying "go get yourself a wife or you'll be lonely"
Student or Learner