Is it appropriate to submit a co-authored writing sample to PhD applications?
I suggest that you don't submit a sample that was written jointly. It would defeat the purpose of the request. The reader doesn't know how you write. I suspect that it would be rejected by many (most?) places.
There are a lot of possibilities for what you might submit. An old assignment, perhaps. Or write up something specifically for this purpose. Perhaps you could write a proposal for some specific research that interests you, showing that you have done some background reading and are looking ahead.