Clustering is a fundamental unsupervised learning technique used to uncover hidden patterns in unlabeled data. Although metaheuristic algorithms have demonstrated effectiveness in clustering, many suffer from premature convergence and limited population diversity. This study employs the Black-Winged Kite Algorithm (BKA) and its enhanced variants, Chaotic BKA (CBKA), Lévy Flight-based BKA (LBKA), and Chaotic Levy BKA (CLBKA), to address these limitations in centroid-based clustering formulated as a Sum of Squared Errors (SSE) minimization problem. Chaotic logistic mapping improves search diversity and adaptability, while Levy flight introduces long-range exploration. In addition, Cauchy based perturbations are incorporated to enhance convergence stability. The algorithms are evaluated on sixteen UCI benchmark datasets, with 30 independent runs conducted under different population and iteration settings. Experimental results show that CLBKA consistently achieves superior clustering performance in terms of accuracy and stability. Statistical validation using the Friedman and Wilcoxon tests confirms significant performance differences, with CLBKA obtaining the lowest mean rank across configurations. The findings indicate that integrating chaotic dynamics and Levy flight mechanisms enhances clustering robustness and optimization efficiency.