Elizabeth Flynn (nee Cotter) was the tenth child born to Michael & Catherine Cotter (nee Dodd). She was born at Taylors Creek, Fish River, NSW on the 1st August 1855.
Fish River is now named Callaba Creek, and it isn't the present location by that name near Gunning. I assume Taylors Creek is a tributary to Callaba Creek (previously Fish River). There is a location named Taylors Flat in that area close by to Narrawa, and there is a Fish River Road near Narrawa, and a Dodd Creek close by.
Michael Cotter was the son of James Cotter, and he was born in either 1809 or 1812 in or around Fermoy in Co. Cork, Ireland.
Catherine Dodd was the daughter of Patrick & Catherine Dodd, she was born in Rathcool, Co. Dublin in 1818.
Hope that helps,