Henry Allen, Jr., an only child, was born to Henry and Juretta Allen, in Algiers, Louisiana (1908), the home base of his father's well known marching band which was formed in 1907 and continued to perform into the early 1950's. He wasted no time in making a career choice; at 8 he was marching with his dad's band and, at age 15, playing with The New Orleans Stompers led by jazz great George Lewis. In 1924 he played in the venerable Excelsior Band and in 1925 co-led a group with John Casimir. Captain John Handy led the house band at the Entertainers' Club and Red joined him for a while ('26) before departing for St. Louis and the St. Louis-Cinncinati riverboat Island Queen. Here he joined The Southern Syncopaters led by Sidney Desvigne.
Allen's career began in Sidney Desvigne's Southern Syncopators. He was playing professionally by 1924 with the Excelsior Brass Band and the jazz dance bands of Sam Morgan, George Lewis and John Casimir. After playing on riverboats on the Mississippi River he went to Chicago in 1927 to join King Oliver's band. Around this time he made recordings on the side in the band of Clarence Williams. After returning briefly to New Orleans, where he worked with the bands of Fate Marable and Fats Pichon, he was offered a recording contract with Victor Records and returned to New York City, where he also joined the Luis Russell band, which was later fronted by Louis Armstrong in the late 1930s.
After being offered a Victor recording contract and jobs by both Duke Ellington and Luis Russell, he returned to New York. He made several recordings under his own name in 1929 for Victor, before joining Luis Russell and his Orchestra, staying with them until 1933. He then joined the Fletcher Henderson Orchestra, replacing Rex Stewart as the group's featured soloist. During this time period Allen made several popular recordings with Coleman Hawkins, where he sang and played trumpet. Starting in 1934 he joined Mills Blue Rhythm Band until he left them in 1937 to rejoin Luis Russell's band which was fronted by Louis Armstrong at that time. He stayed with them until 1940 when he began leading small groups in New York nightclubs and played on records by Jelly Roll Morton, and Sidney Bechet. He continued to record his own records, as well as tour with Billie Holiday, and others throughout the 1940s. In the 1950s and 1960s Red would continue to lead an active career recording with his old friends George Lewis, Coleman Hawkins, and with Kid Ory. Red continued playing up until his death in 1966 from pancreatic cancer.