Complex sentence: After auditioning in Chicago for Andy Kirk's 12 Clouds of Joy, he joined that band and performed with them in the late 1930s and early 1940s; he also spent some time in the US Army during the Second World War.
Split into simpler sentences: After auditioning in Chicago for Andy Kirk's 12 Clouds of Joy, he joined that band and performed with them in the late 1930s and early 1940s. He also spent some time in the US Army during the Second World War.