What about the harmonica that is flattened by a lucky throw from the touchy mare. The harmonica theme is expanded by screenwriters Larry McMurtry and Diana Ossana in the movie. Interestingly, AP chose a similar instrument, the accordion, and focused an entire novel on it, Accordion Crimes.
"Flatness" occurs in the very first part of the story...Jack comes from Lightning Flat. The harmonica is introduced during the mountain scenes, and then flatness comes up again at the end. Jack is "pumping up a flat" when it supposedly explodes and the tire rim hits him in the jaw. He dies by suffocation...blood fills his lungs.
Also, in the prelude of the story, the wind, which has been wailing around Ennis' trailer, temporarily "dies" leaving a brief silence, while Ennis has been dreaming about his old sheepherding partner on the mountain. Does flatness refer to lack of wind (breath)? Or does it mean more than that, the "flattening" that is caused by our being beaten down by life, being "hit by the hammer of life" as AP refers to it?