Hennings spent his childhood in Chicago and often visited and later attended the Art Institute of Chicago. After graduating in 1904, Hennings worked as a commercial artist, muralist, and book illustrator. In 1912 he traveled to Europe and studied under Franz Von Stuck and Angelo Junk at the Royal Academy in Munich, Germany. Hennings returned to Chicago in 1914 and resumed commercial work until former mayor of Chicago Carter H. Harrison, Jr., offered to buy one of his paintings under the condition that Hennings traveled to Taos and become acquainted with the local art community. Harrison instigated similar deals with Hennings' friends William Ufer and Victor Higgins.

Arriving in Taos in 1917, the landscapes, Native Americans, and wildlife of Taos immediately inspired Hennings. His vibrant colors were directly inspired by the bright, natural light of Taos. He permanently settled there in 1921, the same year he became the youngest and penultimate member of the Taos Society of Artists. Hennings worked on many commissions, including paintings of the Navajo Indians in the Rio Grande area for the Santa Fe Railroad.

After his first one man exhibition in Chicago, he married and painted for a year in Europe and Northern Africa. He traveled frequently, maintaining his base in Taos. Just before his death, Hennings completed a series of paintings for the Santa Fe Railway.

Hennings won many awards, including a Gold Medal from the Palette and Chisel Club, the Isidor Gold Medal and the Ranger Purchase Award from the National Academy of Design, the Englewood Women's Club Prize from the Art Institute of Chicago, and the Walter Lippincott Prize from the Pennsylvania Academy of the Fine Arts. His work is recognized in many private collections and museums, including the Pennsylvania Academy of Fine Arts, the Museum of Fine Arts in Houston, the Gilcrease Institute, the Smithsonian American Art Museum, the National Museum of Wildlife Art and the Koshare Indian Museum.