What is referred to in this poem as the "flock" is the people who lived in Father Gilligan's area.  They are the people for whom he, as a priest, is responsible.  The idea is that he is their shepherd and they are his flock -- his group of sheep.

This metaphor comes from the Bible.  Jesus is described as the "Good Shepherd."  He is described as someone who comes and takes care of his sheep.  Therefore, a priest can be described using the same metaphor since a priest is supposed to do Jesus's work as well.