Patrick Blanchflower and Winnefred Ward

Without a more detailed location, i.e. place of birth and/or place of marriage it's going to be difficult to trace these individuals back any further in Ireland. Most of the Catholic and Church of Ireland records for Dublin city are available on the free IrishGenealogy website (the exception is St. Paul's RC). As you may have seen there are a small number of Blanchflower  baptisms, and marriages, along with one death/burial. Two thirds of these are Catholic the remainder Church of Ireland. Do you know what religious denomination your Blanchflower / Ward family were ?

There's just one Patrick Blanchflower mentioned that I see,  married to an Elizabeth Casey in 1790, no sign of a James Blanchflower or a baptism for Michael (b ~ 1826).

The IrishGenealogy website covers all the surviving Church of Ireland records for the City, but only a couple of parishes for County Dublin.Protestant records (i.e. Church of Ireland, Presbyterian, Methodist etc) are not as well covered online as Catholic. Most RC parish registers are available on the NLI website, and indexed by FindMyPast and Ancestry, however note that the dates involved here are very early, very few Catholic parishes have records for the 1700s, and the average starting date for records in rural areas is about 1830.

I searched for possible baptisms for Michael or any possible siblings in Catholic baptism records 1826 +-10, his baptism being the most recent event in Ireland - just one match, Thomas Blanchflower baptised 1830 in Dublin city to parents Thomas and Elizabeth Jones at St. Nicholas RC (Francis Street).

A quick check for possible marriage for Patrick in RC records showed no results, so seems Michael was likely born in a parish were the records start too late, similarly for the marriage of Patrick & Winnifred or the family were not Catholic.