We study the spin dynamics of classical Heisenberg antiferromagnet with nearest neighbor interactions on a quasi-two-dimensional kagome bilayer. This geometrically frustrated lattice consists of two kagome layers connected by a triangular-lattice linking layer. By combining Monte Carlo with precessional spin dynamics simulations, we compute the dynamical structure factor of the classical spin liquid in kagome bilayer and investigate the thermal and dilution effects. While the low frequency and long wavelength dynamics of the cooperative paramagnetic phase is dominated by spin diffusion, weak magnon excitations persist at higher energies, giving rise the half moon pattern in the dynamical structure factor. In the presence of spin vacancies, the dynamical properties of the diluted system can be understood within the two population picture. The spin diffusion of the correlated spin clusters is mainly driven by the zero-energy weather-van modes, giving rise to an autocorrelation function that decays exponentially with time. On the other hand, the diffusive dynamics of the quasi-free orphan spins leads to a distinctive longer time power-law tail in the autocorrelation function. We discuss the implications of our work for the glassy behaviors observed in the archetypal frustrated magnet SrCr$_{9p}$Ga$_{12-9p}$O$_{19}$ (SCGO).
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