The Black-Winged Kite Algorithm (BKA) is a relatively new bio-inspired metaheuristic approach developed to tackle challenging optimization tasks by maintaining a balance between exploration and exploitation. In this context, an improved version of BKA is introduced to better handle complex optimization scenarios. Three modified variants are proposed: CBKA, which incorporates logistic chaos-based mapping to improve solution diversity; LBKA, which utilizes Lévy flight to reinforce global exploration capability; and CLBKA, which merges both mechanisms to enhance the balance between exploration and intensification. The algorithms are assessed on 23 standard benchmark problems spanning unimodal, multimodal, and fixed-dimension test sets. CLBKA achieved the global optimum in 20 out of 23 test functions and ranked first in the Friedman statistical test, with the lowest average rank of 2.9348 among eight algorithms. In addition to the Friedman test, the Wilcoxon signed-rank test was also employed to statistically validate the significance of the observed improvements. Experimental findings indicate that CLBKA consistently outperforms the original BKA and various other metaheuristic techniques in terms of convergence reliability, solution quality, and search stability. Moreover, all proposed algorithms were implemented on six practical engineering design problems, including the Gear Train, Welded Beam, Three-Bar Truss, Pressure Vessel, Tension/Compression Spring, and Cantilever Beam design cases, delivering notably better optimization outcomes. In each case, CLBKA consistently outperformed both its baseline and enhanced variants, as well as several state-of-the-art algorithms from the literature, in terms of solution accuracy, convergence speed, and robustness. The performance of all algorithms was statistically validated using the Friedman test, further confirming the significance and robustness of the proposed hybrid strategies. The results confirm that the proposed hybrid strategies significantly enhance the search efficiency of BKA, making CLBKA a reliable and versatile optimizer for a wide range of complex, constrained optimization tasks.