In 1870-72, John Marius Wilson's Imperial Gazetteer of England and Wales described Falinge like this:
FAILINGE, a hamlet in Spotland township, Rochdale parish, Lancashire; 1 mile W of Rochdale. Pop., with Healey, in 1851, 7, 981; in 1861, 9, 867. Houses, 2, 005. The increase of pop. arose mainly from the prosperity of the cotton trade.
The location is that named as "Falinge Fold" on the modern 1:25,000 map. It is also named, somewhat illegibly, as "Falinge" on our Ordnance Survey First Series map. Additional information about this locality is available for Rochdale
GB Historical GIS / University of Portsmouth, History of Falinge, in Rochdale and Lancashire | Map and description, A Vision of Britain through Time.
Date accessed: 26th March 2017
Click here for more detailed advice on finding places within A Vision of Britain through Time , and maybe some references to other places called " Falinge ".