He was the father of Bruce R. McConkie, a member of the Quorum of the Twelve Apostles of the LDS Church.

In 1914, McConkie began his law studies at the University of Michigan, which led to his son, Bruce, being born in Ann Arbor.

He worked as editor of the San Juan Record, based from Monticello, Utah, where he also practiced law until 1922.

[2] In 1925, McConkie returned to Ann Arbor to finish his law studies at the University of Michigan after which he moved to Salt Lake City in the fall of 1926.

From 1920 to 1923, he was bishop of the Monticello Ward,[5] before becoming a counselor in the presidency of the church's San Juan Stake to Wayne H. Redd, his wife's uncle, from 1923 to 1925.