"The Chrysanthemums" can be read in a feminist context as what Peter Lisca calls a "silent rebellion against the passive role required of her as a woman." This is a good starting point to contextualize the story but it is worth noting that it is not limited to a feminist interpretation. For example, it could be framed as Elisa's frustration with her under-appreciated sexuality; the flowers being a traditional symbol of feminine sexuality.
But, sticking with the feminist idea, the chrysanthemums symbolize Elisa. They also symbolize beauty as well as potential strength and possibility. Given the right care and attention, the flowers can grow to be very beautiful and strong. Henry notes how strong, "ten inches across," they are and the tinker notes how beautiful they are. "Looks like a quick puff of colored smoke?" Elisa appreciates both comments and we can look at these descriptions as parallels with herself. She is beautiful and strong. Ironically, she wants Henry to notice her beauty which he does not, an innocent mistake since he loves her and just looks at the world in practical ways. Elisa wants the tinker to notice her strength and he does not, saying "It ain't the right kind of a life for a woman."
When the tinker leaves, there has been a very subtle sexually charged interaction. But the tinker had only been playing in order to get some work. Later, on the way to dinner, Elisa notices he had thrown out the flowers and kept the pot. The chrysanthemums symbolize opportunity as extensions of Elisa herself. By sharing them with the tinker, the flowers actually travel beyond the confines of the ranch. In a way, a part of her goes on the road with the tinker. This is significant because she tries to convince him that she could do what he does. She feels betrayed by the tinker at the sight of the discarded flowers as if she herself has been cast aside. The tinker has cast aside their shared notions of beauty and the idea that she could compete with him.
In a last ditch effort to assert herself as a strong woman, especially in light of Henry's obliviousness to her attempts to pretty herself up for him, she supposes they go to the fights. But in the end, she retreats from the idea, leaving her dejected again. Had she received the care and consideration (from Henry and/or the tinker) which she had shown the chrysanthemums, her strength and beauty would be more evident to the two men and therefore, more appreciated.