He studied law at Cumberland School of Law at Cumberland University, graduating in 1885, in which year he was admitted to the bar and began practice in Texarkana.
In 1904 he wrote Kirby’s Digest of the Statutes of Arkansas. In 1907 he moved to Little Rock. He was the state"s attorney general from 1907 to 1909, and was elected associate justice of the state supreme court, serving from 1910 to 1916.
He resigned upon his election to the Senate to serve out the term of James P. Clarke, who had died in office.
As a senator, Kirby chaired the Committee on Expenditures in the Department of Agriculture, and served on the Committee on Patents. An unsuccessful candidate for renomination in 1920 and again in 1932, he resumed his law practice upon leaving the Senate.
He again became an associate justice of the state supreme court, serving from 1926 until his death. He died in Little Rock on July 26, 1934, and is buried in Texarkana.
A member of the state House of Representatives in 1893 and again in 1897, Kirby served in the state senate from 1899 to 1901.