What is the likelihood of a young woman getting kidney cancer?

Depends on age: What you consider young, but without symptoms, chances are low.

Relatively uncommon: Kidney cancer is uncommon in young patients (such as under 40 years of age) but it does sometimes occur. Some patients with family history of kidney cancer or an inherited kidney cancer syndrome (such as vhl or von hippel-lindau syndrome) are prone to develop kidney cancer at a younger age than those without.