Fleming was a resident of Tuam, County Galway, and claimed to be a direct descendant of Simon Fleming, 1st Baron Slane (died 1370) was the first Baron Slane.
Ellis Fleming claimed the title in succession to Christopher, 19th Baron Slane, who died in 1771, been a descendant of Christopher, 12th Baron Slane (died 1625), via his third son, John.
Christopher had issue "Six sons, four of whom died without issue ... Thomas, his eldest son, embraced the profession of a friar, and renounced all his right in favour of his brother William."
However, the 14th Baron's last direct male heir, Christopher, died in 1771, which opened the possibility that the descendants of John Fleming could accede to the title.
By that time, descendants of the last baron's female relatives had also issue claims.