The only issue I can think of where a child considers their parent as a BFF is if it is driven by some sort of internal need. This might include attention, favoritism, love, recognition, support, money, sharing of drugs…the list could go on. The driving factor creates a case of manipulation.
My concern is more with the parent who wants to be the BFF of their child, which @zenvelo and @DominicY mentioned.
To answer the other question, yes, it is okay to be friends with your parents once you are an adult and are living on your own. After Dad died, Mom and I took several vacations together because we had the same interests. We really bonded on a different level than we had when I was growing up.