  Systems with engineered flatband spectra are a postulate of high-capacity
transmission links and a candidate for high-temperature superconductivity.
However, their operation relies on the edge or surface modes susceptible to
fluctuations and fabrication errors. While the mode robustness can be enhanced
by a combination of Aharonov-Bohm caging and topological insulation, the design
of the corresponding flatbands requires approaches beyond the standard
$k$-vector-based methods. Here, we propose a synthetic-flux probe as a solution
to this problem and a route to the realization of ultra-stable modes. We prove
the concept in a laser-fabricated graphene-like ribbon photonic lattice with
the band-flattening flux induced by "P" waveguide coupling. The topological
non-triviality is witnessed by an integer Zak phase derived from the mean
chiral displacement. Mode stability is evidenced by excellent mode localization
and the robustness to fabrication tolerances and variations of the input phase.
Our results can serve as a basis for the development of multi-flat-band
materials for low-energy electronics.
