Is taking discounted or free food from KFC, where his relatives work, considered a betrayal of trust, rendering the food unlawful, especially since he swears to repay them?

The employee in the restaurant is a special hired worker (Ajeer Khass), and he is not permitted to take from his employer's money or dispose of it without his permission; otherwise, he would be betraying the trust. If the worker is authorized to dispose of the food, or if your father pays for what he takes, then there is no harm in accepting and consuming that food, because in that case, it is considered a permissible gift. However, if the employee is not authorized, then he is not allowed to take anything unless he pays for it, and whatever he takes without permission remains a debt upon him, and it is not permissible for you to accept what he gives, and you are obliged to pay its price.