During high school, he began to consider the possibility of studying for the priesthood for the Diocese of Corpus Christi. In 1981, he entered Holy Trinity Seminary, an institution associated to the University of Dallas and received a Bachelor of Arts in philosophy in 1983, and a Masters of Divinity in 1987. He completed his preparations for the priesthood in 1988.
In January 1988, he was ordained to the priesthood for the Diocese of Corpus Christi by Bishop Rene H. Gracida. As a priest of the Diocese of Corpus Christi, he served in a number of capacities, including Parochial Vicar at Corpus Christi Cathedral, Secretary to the Bishop, Diocesan Master of Ceremonies, Assistant Chancellor, Rector of the Saint John Vianney House of Studies, and Episcopal Vicar for Vocations. In September 1995, Pope John Paul II named him a Chaplain to His Holiness, with the honorary title of Monsignor. In September 1997, he was sent by Bishop Roberto Gonzalez, OFM, to Rome to pursue a doctoral degree in the theology of Saint Thomas Aquinas. Bishop Flores resided at the North American College, Casa Santa Maria in Rome, while studying at the Pontifical University of St. Thomas Aquinas (the Angelicum). He completed his degree (S.T.D.) in 2000 and returned to Corpus Christi that year, and was appointed Chancellor of the Diocese of Corpus Christi by Bishop Edmond Carmody.
In August 2001, he was sent to serve in the Archdiocese of Galveston-Houston as part of the formation faculty of St. Mary’s Seminary and the teaching faculty at the University of St. Thomas School of Theology, in Houston, Texas. He taught courses in Patristics, Medieval and Thomistic Theology, and Modern Catholic Literature. He was named Vice-Rector of St. Mary’s Seminary in June 2002. In September 2005, Bishop Edmond Carmody named him to serve as Rector of Corpus Christi Cathedral, in Corpus Christi, Texas. During the months of the scholastic year 2005-2006, he administered Corpus Christi Cathedral while completing his seminary duties in Houston, Texas. In June of 2006, he returned to the Diocese of Corpus Christi to assume the position of Cathedral Rector on a full time basis.
In October 2006, Pope Benedict XVI named him Auxiliary Bishop for the Archdiocese of Detroit, in Michigan. He was ordained on November 29, 2006, in a ceremony presided over by Adam Cardinal Maida, Archbishop of Detroit. Recognizing the growing population of Catholics of Hispanic heritage in the Archdiocese of Detroit, Cardinal Maida named Bishop Flores to oversee Hispanic ministry in the Archdiocese. At the same time, he gave his responsibility over a region of the Archdiocese, and directed him to teach theology at the Archdiocesan Major Seminary (Sacred Heart Major Seminary). With time, he was assigned as Episcopal liaison to the Cardinal for Black Catholic Affairs in the Archdiocese of Detroit, and moderator of matters related to Catholic hospitals in the Archdiocese. Bishop Flores continued with these responsibilities under the direction of Archbishop Allen Vigneron, who was named Archbishop of Detroit in January, 2008.
On December 9, 2009, Pope Benedict XVI appointed Bishop Flores as the Sixth Bishop of Brownsville. He was installed on February 2, 2010 at the Basilica of Our Lady of San Juan del Valle – National Shrine, and thus became the third native Texan to serve the Rio Grande Valley as Bishop.
On a national level, as a member of the United States Conference of Catholic Bishops (USCCB), Bishop Flores currently serves as Chairman of the Committee on Cultural Diversity in the Church. He also serves as a member to the following committees: Ad Hoc Committee for Religious Liberty, Committee of Divine Worship, Sub-Committee on Pro-life Activities, and the Committee for Ecumenical and Inter-Religious Affairs. He is also a member of the Board of Directors of Catholic Relief Services (CRS), the charitable arm of the United States Bishops Conference for international assistance.