How does 1,3-dichloro-1,3,5-triazinane-2,4,6-trione (dichloroisocyanuric acid) generate hypochlorous acid when dissolved in water?
$\ce{N-Cl}$ bond is polarized toward nitrogen: $\ce{N^--Cl+}$ This means, that any chloramine can produce $\ce{HOCl}$ in water by mean of hydrolysis of $\ce{N-Cl}$ bond. 

$$\ce{R2NCl + H2O -&gt; R2NH + HOCl}$$

The mechanism is more subtle matter. Basically, it should be one of $S_N$ mechanisms, but it is hard to choose right one here ($S_N1$ or $S_N2$). The central atom in mechanism here should be $\ce{Cl}$, and $\ce{R2N-}$ is leaving group.