Looking at the early census, parents Peter and Hannah and eldest three children (William, John and Mary) all born in Dublin. Have you looked at the RC Ireland Parish Registers?
This looks like son John's baptism for example:
John Flannagan
Birth 1849 and bptsm. 7 Jan 1849 at St James', Dublin city, Dublin
Father: Peter Flannagan
Mother: Hanna Flynn
Also shows on the parish registers here
www.irishgenealogy.ie/en/ No image for John's entry but additional details such as witnesses etc.
Monica
