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Records for Killarney parish go back to 1785. Since the marriage was in 1812, John and Catherine were likely born around 1790-1795. However, when I searched on the subscription site Roots Ireland there were no John Flynn or Catherine Garin baptismal records in the late 1700s.
Did you see the baptismal records for Patrick 1815 Daniel 1817 Matthew 1823? The record for Patrick shows Mary Garin. The other two records show Catherine Garin.