  We propose a general strategy for generating synthetic magnetic fields in
complex lattices with non-trivial connectivity based on light-matter coupling
in cold atomic gases. Our approach starts from an underlying optical flux
lattice in which flux arises by coupling several internal states. Starting from
a high symmetry optical flux lattice, we superpose a scalar potential with a
super- or sublattice period in order to eliminate links between the original
lattice sites. As an alternative to changing connectivity, the approach can
also be used to create or remove lattice sites from the underlying parent
lattice. To demonstrate our concept, we consider the dice lattice geometry as
an explicit example, and construct a dice lattice with a flux density of half a
flux quantum per plaquette, providing a pathway to flat bands with a large band
gap. While the intuition for our proposal stems from analysis of deep optical
lattices, we demonstrate that the approach is robust even for shallow optical
flux lattices far from the tight-binding limit. We also provide an alternative
experimental proposal to realize a synthetic gauge field in a fully frustrated
dice lattice based on laser-induced hoppings along individual bonds of the
lattice, again involving a superlattice potential. In this approach, atoms with
a long-lived excited state are trapped using an 'anti-magic' wavelength of
light, allowing the desired complex hopping elements to be induced in a
specific laser coupling scheme for the dice lattice geometry. We conclude by
comparing the complexity of these alternative approaches, and advocate that
complex optical flux lattices provide the more elegant and easily generalisable
strategy.
