Is it permissible for an uncle to give his nephew from his Zakat, knowing that the father provides for his son and secures all his needs?

If the son receives sufficient support for his needs and housing, it is not permissible to give him zakat on the basis of him being poor or needy. However, if giving him zakat is for another reason, such as him being in debt (ghārim), then it is permissible. And Allah knows best.