The problem is the subject. "Falling Flowers" suggests these warriors are knowingly going to their deaths, but who are they? If taken from war chronicles like The Tales of Heike, what scene does it illustrate? I thought I'd managed to narrow down the theme to the "Death of Kiso" episode of The Tale of the Heike, but after reading several versions of this scene, now I am not sure.
By the description given in the "Death of Kiso" text, Kiso (Minamoto) Yoshinaka wore "a red brocade hitatare robe under a suit of finely laced armor, and a hoe-shaped (kuwagata) helmet on his head. For weapons, he bore a massive sword at his side, a rattan-bound bow in his hand…" Based on this, I'm guessing the that the figure on the far left is Yoshinaka (even though I am not sure about the helmet, which Burton Watson and Helen McCullough both translate as "horned," perhaps in reference to the Kuwagata beetle). But the distinctive black, rattan-bound bow is in his hand, so I feel I am pretty safe identifying this figure as Kiso. The female figure on the far right, based on the tomoe-mon on her robe, I've identified as Tomoe Gozen, who was known as Kiso's constant companion (which also helps confirm the ID of Kiso himself).
The problem is the center figure, who is clearly the focus of the painting. If this was the "Death of Kiso" episode, then Yoshinaka should take center stage, not be pushed to the far left. Also, as far as I can tell, the Tales of Heike text make no mention of a figure garbed this way. He carries a naginata spear (often associated with women warriors, but not exclusively). He's shown with pale white features used to mark beautiful youths, and his hair is cut shoulder-length, not left long - in other words, this is not a woman but a young man. He wears a long juzu around his neck, which must signify something. But most obviously is the long gauzy cape or shawl that is caught on the horse's bridle and drapes over the rider's head and torso.
My research is ongoing, but at this point, my best guess is it is a scene from Tale of Heike, not the Death of Kiso scene but another, in which both Yoshinaka and Tomoe Gozen appear but do not die, and only this central youthful figure rides to meet his end (someone has to die, based on the title of the painting...).