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 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...