The rising action structurally follows the Introduction, which is when the central characters, Catherine and Frederic Henry, meet and unfold their relationship to each other along with the beginnings of the story conflict. In A Farewell to Arms, since it is, according to Hemingway, a love story, at least part of the conflict--or one of the aspects of conflict--is the difficulty of attaining an intimate, loving relationship during the horrors of world war versus the idealized image of its attainment.
Since the romance, by Hemingway's design, as stated by Edmund Wilson, is Hemingway's Romeo and Juliet, the flirtation and building romance between Henry and Catherine comprise the rising action that leads up to Henry's need to return to the front. The rising action of their flirtation builds in Chapter 14, then becomes earnest from Chapter 15 when Dr. Valentini examines him and schedules surgery.
[Romeo and Juliet remark quoted by Edmund Wilson in "Ernest Hemingway: Bourdon Gauge of Morale" first printed in Atlantic Monthly 164 (July 1939).]