  Kagome lattice is a two-dimensional network of corner-sharing triangles and
is often associated with geometrical frustration. In particular, the frustrated
coupling between waveguide modes in a kagome array leads to a dispersionless
flat band consisting of spatially localized modes. Here we propose a complex
photonic lattice by placing $\mathcal{PT}$-symmetric dimers at the kagome
lattice points. Each dimer corresponds to a pair of strongly coupled
waveguides. With balanced arrangement of gain and loss on individual dimers,
the system exhibits a $\mathcal{PT}$-symmetric phase for finite gain/loss
parameter up to a critical value. The beam evolution in this complex kagome
waveguide array exhibits a novel oscillatory rotation of optical power along
the propagation distance. Long-lived local chiral structures originating from
the nearly flat bands of the kagome structure are observed when the lattice is
subject to a narrow beam excitation.
