[1] After graduating from college, Flesey entered Immaculate Conception Seminary at Seton Hall University in South Orange, New Jersey, remaining there until 1969.
During this period, he received a Master of Pastoral Counseling degree from Iona College in New Rochelle, New York, and a Bachelor of Sacred Theology degree from Catholic University of America in Washington, D.C.[2][1] On May 31, 1969, Flesey was ordained a priest by Archbishop Thomas Aloysius Boland for the Archdiocese of Newark.
[1][3] After his ordination, Flesey was assigned to pastoral work at St. Bernard of Clairvaux Parish in Plainfield, New Jersey, spending 14 years there.
[2] In 1990, Flesey returned to Rome to obtain his Doctor of Sacred Theology degree from the Pontifical University of Saint Thomas Aquinas.
He was consecrated at Cathedral Basilica of the Sacred Heart in Newark, New Jersey, by Archbishop John Myers on August 4, 2004.