In 1946, Fleniken was named assistant U.S. Attorney under Malcolm Lafargue, who left the position in May 1950 to run unsuccessfully in the Democratic primary election against U.S. Senator Russell B. Long.
After his work as U. S. attorney, Fleniken resumed the practice of law under the name Brown & Fleniken, with partner Algie D. Brown, a member of the Louisiana House of Representatives from 1940 to 1968.