  We study the flux noise $S_{\Phi}(\omega)$ and finite frequency conductivity
$\sigma_1(\omega)$ in two dimensional unfrustrated Josephson junction arrays
(JJA's), by numerically solving the equations of the coupled overdamped
resistively-shunted-junction model with Langevin noise. We find that
$S_{\Phi}(\omega)\propto \omega^{-3/2}$ at high frequencies $\omega$ and
flattens at low $\omega$, indicative of vortex diffusion, while $\sigma_1
\propto \omega^{-2}$ at sufficiently high $\omega$. Both quantities show clear
evidence of critical slowing down and possibly scaling behavior near the
Kosterlitz-Thouless-Berezinskii (KTB) transition. The critical slowing down of
$S_{\Phi}$, but not its frequency dependence, is in agreement with recent
experiments on Josephson junction arrays.
