https://www.familysearch.org/s/search/index/tree-search#searchType=trees&fed=true&collectionId=&advanced=false&exact-givenName=on&givenName=&exact-surname=on&surname=FlenleyGives a possible WILLIAM F. BORN 1754.
http://trees.ancestry.co.uk/pt/RequestTreeAccess.aspx?tid=10670083&pid=1227799118has a private Tree with him and family in it'
a more likey one for rhe workhouse master is his son, William F b.1780, right age for the death Shane found.
Married Eliza Horne. may be this couple:
Marriage: 1806 Nov 16 — St. Giles-In-The-Fields, London, England
One son, Henry b. Dublin
Henry Michael FLENLEY
gender: Male
birth: 1819 Apr 29
Dublin, Ireland
christening: 1819 May 23
Dublin, Ireland
death: 1872 Jun 29
Tarnagulla, Victoria, Australia
burial: 1872 Jul 2
Tarnagulla, Victoria, Australia
afn: HJ06-B5
spouse: Mary Anne ARDERN (AFN: )
marriage: 1848 Oct 28
St. Michael's Toxteth, Walton-On-The-Hill, Lancaster,
There are several other children:
William Henry FLENLEY
Ancestral File
birth: 1817 —
parents: William FLENLEY, Eliz. HORNE
John FLENLEY
Ancestral File
birth: 1821 —
parents: William FLENLEY, Eliz. HORNE
Edgar FLENLEY
Ancestral File
birth: 1822 —
parents: William FLENLEY, Eliz. HORNE
George FLENLEY
Ancestral File
birth: 1824 —
parents: William FLENLEY, Eliz. HORNE
Thomas Howe FLENLEY
Ancestral File
birth: 1826 —
death: 1827
parents: William FLENLEY, Eliz. HORNE
Edmund Patrick FLENLEY
Ancestral File
birth: 1829 —
parents: William FLENLEY, Eliz. HORNE
Emily Jane FLENLEY
Ancestral File
birth: 1830 —
parents: William FLENLEY, Eliz. HORNE
Charlie FLENLEY
Ancestral File
birth: 1831 —
parents: William FLENLEY, Eliz. HORNE
Don't know if this ties in with your family, but for what its worth, being a submitted entry, here it is. PM easy enough to check out some of the citations.