  Emerging experimental platforms use amorphousness, a constrained form of
disorder, to tailor meta-material properties. We study localization under this
type of disorder in a class of $2D$ models generalizing recent experiments on
photonic systems. We explore two kinds of localization that emerge in these
models: Anderson localization by disorder, and the existence of compact,
macroscopically degenerate localized states as in many crystalline flat bands.
We find localization properties to depend on the symmetry class within a family
of amorphized kagom\'{e} tight-binding models, set by a tunable synthetic
magnetic field. The flat-band-like degeneracy innate to kagom\'{e} lattices
survives under amorphousness without on-site disorder. This phenomenon arises
from the cooperation between the structure of the compact localized states and
the geometry of the amorphous graph. For particular values of the field, such
states emerge in the amorphous system that were not present on the kagom\'{e}
lattice in the same field. For generic states, the standard paradigm of
Anderson localization is found to apply as expected for systems with
particle-hole symmetry (class D), while a similar interpretation does not
extend to our results in the general unitary case (class A). The structure of
amorphous graphs, which arise in current photonics experiments, allows exact
statements about flat-band-like states, including such states that only exist
in amorphous systems, and demonstrates how the qualitative behavior of a
disordered system can be tuned at fixed graph topology.
