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. In 1983, he entered the Pontifical Gregorian University in Rome, obtaining a Licentiate in Sacred Theology in 1985. Returning to New Jersey, Flesey was assigned to Immaculate Conception Seminary as a faculty member.[2]
In 1990, Flesey returned to Rome to obtain his Doctor of Sacred Theology degree from the Pontifical University of Saint Thomas Aquinas. Back in New Jersey, he returned to teaching at the seminary and in 1995 was appointed rector, serving for five years. After a sabbatical year in Italy, Flesey was appointed director of ongoing formation for the priests in the archdiocese.[2][1] He also returned to work at the seminary as spiritual director.[4]
On October 16, 2017, Pope Francis accepted Flesey's letter of resignation as auxiliary bishop of Newark, submitted when Flesey reached the mandatory retirement age of 75, as required under canon law.[5][3]