  We consider a model for a two-dimensional Kagome-lattice with defocusing
nonlinearity, and show that families of localized discrete solitons may
bifurcate from localized linear modes of the flat band with zero power
threshold. Each family of such fundamental nonlinear modes corresponds to a
unique configuration in the strong-nonlinearity limit. By choosing well-tuned
dynamical perturbations, small-amplitude, strongly localized solutions from
different families may be switched into each other, as well as moved between
different lattice positions. In a window of small power, the lowest-energy
state is a symmetry-broken localized state, which may appear spontaneously.
