County Kilkenny, Parish Coolagh - Unable to find on Church of Ireland Parish Register

I suspect the parish is more commonly known as Coolaghmore (Mór just meaning big). The townland is probably also known as Ballyfliugh. Spelling varies in Ireland. I see 3 Fleming farms there in Griffiths Valuation:

https://www.askaboutireland.ie/griffith-valuation/index.xml?action=nameSearch

2 Fleming families farming there in 1901:

https://www.census.nationalarchives.ie/pages/1901/Kilkenny/Mallardstown/Ballyfliugh/

Note that both families were Roman Catholic (you mention searching the Church of Ireland records, so perhaps these may not be the ones you are looking for).

As far as I can see Coolaghmore/Coolagh civil parish came under Callan for both Catholic and Church of Ireland records.

The Catholic records for the parish start 1821 and include some Fleming baptisms, however these children would all be a little too young to hold land at the time of the Tithe Applotments (30th June 1827). There is a couple named James Fleming and Cath Grace who have at least one child baptised in the parish Union during this time - a Margaret Fleming bapt. 4th September 1828

Early Church of Ireland records for Callan Parish Union are listed as lost - earliest available seem to be from about 1892 onward