Why are chrysanthemums rather than another flower like a rose used in this story?
There are several possibilities:
Steinbeck could've used Chrysanthemums because they are such a popular flower that bloom in the fall and have long lived blooms (which is why florists love them).
But I think more is going on here. First is the fact that Chrysanthemums require attention - they need fertile, well drained soil and sunshine. To Elisa her flowers are like her children, and she mothers over them carefully. When the tinker asks her about her flowers, she responds like a proud parent. But Elisa is like the Chrysanthemum herself - she also needs a fertile, sunny environment in which to bloom. But she finds herself trapped, a potted flower in poor soil and dim light.
At the end of the story, she does try to dress up to impress her husband, putting on a bright and pretty dress. But Henry doesn't really appreciate her efforts, doesn't appreciate her pretty bloom.
Finally, Chrysantheums bloom in the fall - they are a like a lingering hope, a fading echo of spring, the last gasp of flowering life before the cold darkness of winter. This may also reflect Elisa's desire to bloom, but is also may foreshadow the coming winter in their relationship. Henry just isn't a gardener, not in real life, and not metaphorically with his wife.
Chrysanthemums are shaped like a star. They have a round center with pointy petals sticking out all around it. When she explains to the tinker man what it is like sleeping out in the stars, she describes the sensation like a sexual act, the imagery suggesting both stars and the flower. The chrysanthemum is an appropriate symbol for such sexuality because it, unlike the rose, is not associated with romance. It is earthier, stronger. In addition, its very appearance suggests sexuality, while the rose, beautiful and romantic, has a different sort of shape, not indicative of sexual body parts.