Hello Jean, This is all I found that is conclusively about John W. Pipkin, son of Francis Marion and Martha Pipkin. There were other J. W. Pipkins and I believe most of them were around Dobbs County, North Carolina and from Virginia before that.
I am sorry I can't go further back, and hope that you are able find what you are looking for. If you are not certain and want me to look for other Pipkins in MS I would be happy to do more digging for you.
1860 United States Federal Census ancestry.com Name: John W Pipkin Age in 1860: 21 Birth Year: abt 1839 Birthplace: Mississippi Home in 1860: Franks, St Francis, Arkansas Gender: Male Post Office: Madison Household Members: NameAge Adison Farrow39 Elizabeth Farrow35 William Farrow14 Mary J Farrow13 Francis M Farrow10 Martha Farrow8 Richard Farrow6 Virginia Farrow5 Elizabeth Farrow3 Patrick R Farrow4/12 John W Pipkin21
I found it interesting that this Farrow family named one of their children Francis M. I assume after Mr. Pipkin.