Let's come to your second question here as it is easier: the word "one" here refers to "a woman", according to the context. (Flirting is a woman's trade, one must keep in practice.)
As to your first question, "someone's trade" (roughly) means something that he or she depends on for a living. So, according to this sentence, the speaker thinks that a woman depends on flirting for a living, so she must keep practicing it.
I hope this can help you understand.