Kidney exchange programs have substantially increased transplantation rates but also raise critical concerns about fairness in organ allocation. We propose a novel framework leveraging Data Envelopment Analysis (DEA) to evaluate multiple dimensions of fairness-Priority, Access, and Outcome-within a unified model. This approach captures complexities often missed in single-metric analyses. Using data from the United Network for Organ Sharing, we separately quantify fairness across these dimensions: Priority fairness through waitlist durations, Access fairness via the Living Kidney Donor Profile Index (LKDPI) scores, and Outcome fairness based on graft lifespan. We then apply our conditional DEA model with covariate adjustment to demonstrate significant disparities in kidney allocation efficiency across ethnic groups. To quantify uncertainty, we employ conformal prediction within a novel Reference Frontier Mapping (RFM) framework, yielding group-conditional prediction intervals with finite-sample coverage guarantees. Our findings show notable differences in efficiency distributions between ethnic groups. Our study provides a rigorous framework for evaluating fairness in complex resource allocation systems with resource scarcity and mutual compatibility constraints.