  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).
