Catch-22 as a whole has a nonlinear timeline, meaning its events happen out of chronological order. This means there are flashbacks and reminiscences of many kinds throughout the novel, as Yossarian discusses his and others' pasts at many different points. The most extended flashback, though, is the description of the Battle of Bologna, which begins in Chapter 12 and carries on through Chapter 20.
The Battle of Bologna, in the fictional version of World War II in Catch-22, is among the first events in the chronological timeline. (There was a real-life Battle of Bologna, but it occurred near the end of the war in April 1945 and was mostly a ground conflict.) The reader first learns of the battle when Yossarian artificially constructs its end, by moving a line on a battle map. In later chapters, readers find out more about the siege of the city and the characters' time on mainland Italy: de Coverly's disappearance in Chapter 13 and Orr's in Chapter 14; the beginning of the conflict between Aarfy and Yossarian in Chapter 15; and the interactions with the Roman prostitutes in Chapters 16 and 17. So the story is told out of order in the largest sense, in that the consequences of the Battle of Bologna are described before the battle itself. And furthermore, in typical Heller style, once the battle is described, the ending (which occurs under an ironic situation) is described first.
The system of flashbacks works to cushion the reader from the violence of the war. Heller seeks to make the war seem absurd, full of illogical, uncritical, stupid officers. The timeline makes the war seem far away, making the violence seem even more absurd and paradoxical. When the specifics of the battle are revealed in their own nonlinear way, the notion of absurdity becomes more complex.