Irish Flax Growers, 1796

I have found my great-grandfather 3x removed Patrick McMullen was a Flax Dealer in 1862 Belfast.  He was born 26 Mar 1813 • Belfast, Antrim and married on 28 Sep 1823 • St Patrick's, Belfast city to Sara Ann Walsh.  All of their children were born in Belfast between 1831 and 1843 and came to live in Manchester, England soon after that date.  

I'd love to find out anything more about the family particularly Patrick and Sara but can't pin down what area of Belfast they lived. I have found a Flax Growers List for 1796 https://www.failteromhat.com/post1796.php with 2 McMullen's listed.  Patrick's father was John Patrick b.1791 so there is a possiblity he was one of the 2 McMullen's on that list in Ballintoy, otherwise no more clues.

Any clues would be very welcome.