What are the major conflicts in "The Chrysanthemums"?

The opening description of Elisa strongly suggests that she is an extremely capable woman whose potential is not being fully tapped on the farm where she lives. The house is aggressively maintained, as are her chrysanthemums. When she and Henry talk about her gardening ability, she indicates that she could find the same success in their orchard, but the conversation goes no further. It seems symbolic that she is inside an ornamental flower bed surrounded by a wire fence, and that she expresses her distaste for "fights." Elisa may feel fenced in and have aspirations beyond her current situation, but she isn't able or willing to fight to achieve them.

In Elisa's conversation with the tinker, she asserts herself as capable and openly admires his freedom to travel at will. He argues that the way he lives would not be suitable for a woman. In the end, he gets the work that he came for when Elisa relents and gives him two pans to mend, but only after he has flattered her by feigning interest in her chrysanthemums. Perhaps in Steinbeck's view, it is a transaction that symbolizes how women get along in life, acquiescing to the power that men hold over them.

The most important conflict in the story is the limitation of Elisa's life as a woman isolated on a small farm in the Salinas Valley in the years after the Depression. Confined by gender roles to work within the boundaries of the farm while the men enjoy more freedom and mobility, Elisa's longings are awakened when the tinker comes by and describes his journeyman lifestyle. She responds wistfully, "That sounds like a nice way to live".

A second major conflict is Elisa's deep aesthetic approach to life which cannot be shared. Her husband Henry, a good man who loves his wife, unfortunately sees everything from a functional point of view. Elisa's attempts to dress up and make herself pretty are lost on him, as are her efforts to get him to appreciate the astounding beauty of her beloved chrysanthemums, the expression of her aesthetic sense.  Elisa's hunger to share this essential part of her nature is such that, when the tinker appears to understand her passion for her flowers, she responds with an excitement that approaches the sublime. Sadly, when she discovers that he has discarded the chrysanthemum she gave him carelessly on the road, she realizes that his interest was contrived, and is left more alone and frustrated than before.

What incidents complicate the conflict and reveal the climax in "The Chrysanthemums"?

Elisa, the main character in this story, has an internal conflict.  She struggles with her love for aesthetic beauty and desiring her husband to see and recognize it, not only in her flowers, but in HER.  Her husband is a good one and works hard on the farm, but he sees her flowers as nothing more than a great body of work...meaning he is impressed by the sheer number of them and how hard she works.  He does not appreciate their beauty.  Elisa wishes that he did, however.

The pot-mender that comes along flatters Elisa with compliments about her flowers and he flirts with her in subtle ways using that flattery.  This complicates her internal conflict because only later does she become aware that the pot-mender was a liar and was only trying to get some pots to mend.  He had no interest in her flowers, but she THOUGHT he did.

The climax occurs at the end of the story when she spots the chrysanthemum on the road.  The pot-mender had dumped it out on the road and saved the pot.

eNotes states:

Although the narrator, Henry, and Elisa have all praised her for her strength, she is not strong enough to overcome her limitations, and she breaks down in weak tears ''like an old woman.''