Is it permissible to give a nursing wife's milk to a cancer patient as a treatment?

The jurists are in consensus regarding the purity of human milk.

Drinking a woman's milk does not establish mahramiyyah (prohibition of marriage) except under two conditions: that it occurs within the first two years (of the child's life), and that there are five or more distinct sucklings.

It is permissible to use a woman's milk for medicinal treatment, whether by drinking, injection, or instillation.

Therefore, there is no harm for a woman to give milk to someone who requests it for treatment, because it is pure and permissible.