The paper presents a multi-kernel SVM-supported federated learning framework for β-thalassemia carrier prediction that protects patient privacy by training models locally in clinics and sharing only model parameters. This approach addresses centralized screening issues such as GDPR and HIPAA restrictions. The model uses linear, polynomial, radial basis functions and a deep kernel, aggregating updates by federated averaging. Explainable AI methods SHAP and LIME reveal important hematological characteristics such as hemoglobin level and mean corpuscular volume. On 5,066 complete blood count records, the model achieved an accuracy of 98.4%, a sensitivity of 99.2%, and a specificity of 98.8%, comparable to centralized methods. The results enable scalable screening in distributed healthcare systems while preserving privacy.