We report the dynamical magnetic properties of the $s=\frac{3}{2}$ kagome ferromagnet ${\mathrm{Li}}_{9}{\mathrm{Cr}}_{3}{({\mathrm{P}}_{2}{\mathrm{O}}_{7})}_{3}{({\mathrm{PO}}_{4})}_{2}$ using magnetic susceptibility, specific heat, electron spin resonance (ESR), and nuclear magnetic resonance techniques. The magnetic susceptibility and specific heat show ferromagnetic ordering at ${T}_{\mathrm{C}}=2.7$ K. The in-plane ferromagnetic correlation length ${\ensuremath{\xi}}_{ab}$ deduced from the magnetization curves reveals that ${\ensuremath{\xi}}_{ab}$ increases steeply from 18.2 to 41.3 \AA{} as the temperature is lowered from 50 K to ${T}_{\mathrm{C}}$, indicative of the persistence of two-dimensional magnetic correlations up to temperatures as high as $\ensuremath{\sim}18\phantom{\rule{0.16em}{0ex}}{T}_{\mathrm{C}}$. The ESR linewidth $\mathrm{\ensuremath{\Delta}}{H}_{\mathrm{pp}}$ and magnetic specific heat data indicate a change in spin dynamics at about ${T}^{*}\ensuremath{\approx}4.4{T}_{\mathrm{C}}$. Intriguingly, for temperatures below 50 K, we observe an unexpected suppression of the $^{7}\mathrm{Li}$ spin-lattice relaxation rate $1/{T}_{1}$. The decrease in $1/{T}_{1}$, which occurs well above ${T}_{\mathrm{C}}$, is at odds with the critical slowing down of magnetic correlations typically observed in conventional ferromagnets. This anomalous thermal evolution of spin fluctuations is interpreted in terms of the concerted interplay of flat and Dirac magnon bands inherent in kagome ferromagnets.