This work studies knowledge distillation (KD) for large language models (LLMs) through preference optimization. We propose a reward-guided imitation learning framework for sequential KD, formulating a min-max optimization problem between the policy and reward model (RM) to minimize the performance gap between the student and teacher policies. Specifically, the reward optimization is constrained to achieve near-optimality within a confidence set for preference alignment. For preference data construction, we explore both offline and online preference-based KD. Additionally, we reformulate the RM using the Q-value function and extend the framework to white-box KD, where the teacher policy's predicted probabilities are accessible. Theoretical analysis and empirical results demonstrate the effectiveness of the proposed framework.