Electronic health records (EHRs) support strong clinical prediction but often provide coarse, post hoc explanations that are hard to use for patient-level decisions. We propose a knowledge-graph (KG)-guided chain-of-thought (CoT) framework for visit-level disease prediction on MIMIC-III. We map ICD-9 codes to PrimeKG, mine disease-relevant nodes and paths, and use these paths to scaffold temporally consistent CoT explanations, retaining only samples whose conclusions match observed outcomes. We then fine-tune lightweight LLaMA-3.1-Instruct-8B and Gemma-7B models on two small cohorts (400 and 1,000 index visits) across ten PrimeKG-mapped diseases. Our models outper-form strong classical baselines, reaching AUROC of 0.66-0.70 and macro-AUPR of 0.40-0.47. Without additional training, the models transfer zero-shot to the CRADLE cohort, improving accuracy from 0.40-0.51 to 0.72-0.77. Blinded clinicians consistently prefer KG-guided CoT for clarity, relevance, and correctness. Code is available at https://github.com/JonathanWry/KG-guided-LLM-pipeline.