BALTIMORE, Md. — The Winona-Rochester Catholic bishop, Robert Barron, will not be the new president — or vice president — of the influential U.S. Conference of Catholic Bishops. Barron had been nominated, but Archbishop Paul Coakley of Oklahoma City and Bishop Daniel Flores of Brownsville were chosen. Both are senior to Barron in church hierarchy; Coakley, age 70, was first a bishop in 2004; Flores, age 64, first a bishop in 2010; and Barron, age 66, first a bishop in 2022. Barron, however, is the most prominent for his “Word on Fire” television and online ministry. Also he is occupied currently with a major liturgical translation.