  We study the quench dynamics on cross-stitch flat band networks by a sudden
change of the inter-cell hopping strength $J$. For quench processes with $J$
changing as $J=0\rightarrow J\neq0$, we give the analytical expression to the
Loschmidt echo which possesses a series of zero points at critical times
$t^{*}$, indicating where the dynamical quantum phase transitions occur. We
further study the converse quench process with $J\neq0\rightarrow J=0$, and
find a non-trivial example that the pre-quench quantum state is not an
eigenstate of the post-quench Hamiltonian, whereas the Loschmidt echo
$\mathcal{L}(t)\equiv1$ during this process. For both situations, these results
are also illustrated numerically. Finally, we give a brief discussion on the
observation of these predictions in the system of ultracold atoms in optical
lattices.
