In a second-best optimal growth setup with only factor taxes as available instruments, is it optimal to fully replace capital by labor income taxation? The answer is generally positive based on Chamley, Judd, Lucas, and many follow-up studies. In the present paper, we revisit this important tax reform-related issue by developing a human capital-based endogenous growth framework with frictional labor search and matching. We allow each firm to create multiple vacancies and each worker to determine labor market participation endogenously. We consider a benevolent fiscal authority to finance direct transfers to households and unemployment compensation only by factor taxes. We then conduct dynamic tax incidence exercises using a model calibrated to the U.S. economy with a pre-existing 20% flat tax on both the capital and labor income. Our numerical results suggest that, due to a dominant channel via the interactions between the firm's vacancy creation and the worker's market participation, it is optimal to switch partly by a modest margin from capital to labor taxation in a benchmark economy where human capital formation depends on both the physical and human capital stocks. When the human capital accumulation process is independent of physical capital, the optimal tax mix features a slightly larger shift from capital to labor taxation; when we remove the extensive margin of the labor-leisure trade-off, such a shift is much larger. In either case, however, the optimal capital tax rate is far above zero.