Dancer, is Mount East County, Queens/Laois? I've never heard of that Mountrath yes? A new piece of information.
If so then is father John Flynn in Laois for the 1901 Census? There are 48 John Flynn's in Laois.
I have civil registrations from 1864-1875 if any of her siblings may have been born within that town frame, these come with mother's name and maiden name. There are a number born with a father John at Mountmelick, Queens
Also any births from 1864 would be recorded on www.familysearch.org
(but often without parents names)www.irishgenealogy.ie
Anne Flynn born 1888 noted no record of month or day
Father - Flynn but no name
Mother - Ann Flynn
Witness 2 - Sarah Brennan
Address: 22 Townsend St. Dublin
St. Andrews (Dublin) RC
The marriage where you give the same church is not listed
but likely because of the date. Most genealogy resources
only go to 1899!