Chrysanthème is indeed a flower (see it here).

In France, On November 1st, there is the “Toussaint“. It started off as a religious celebration but now it’s more or less for everyone. To sum up, this celebration is for the Dead, and the Chrysanthème is the flower associated with it since the 19th. So while “De Chrysanthème en Chrysanthème” isn’t a phrase, it still has meaning.

_{La Toussaint (1886), par Émile Friant}

This is a flower equivalent to the Chysanthemum.

As seen in a English to French Dictionary
chrysanthemum
n chrysanthème m

http://en.wikipedia.org/wiki/Chrysanthemum

It is a figure of speech, in which the “chrysanthèmes”, flowers of death, represent a burial.

“De chrysanthèmes en chrysanthèmes” = “From one burial to another burial”

This figure of speech is called a “metonymy”, in which a word is replaced by another one somehow linked with it.

Common examples:

• “The crown” for “the monarchy”
• “Downing Street” for “the prime minister”
• “The bottle” for “the alcohol”
• Idiomatic expression “Le sabre et le goupillon” : The traditional alliance between the Catholic Church and the French army (“le sabre” = the sword; “le goupillon” = a kind of brush used by the priest to sprinkle holy water on people)