Knitted fabrics exemplify a broad class of flexible material systems that accommodate large deformations, providing rich mechanisms to potentially achieve shape morphing, embedded sensing functionality, and mechanical biocompatibility without material damage. Although geometric nonlinearity has been intuitively utilized in their design analogously to architected materials, a quantitative framework that prescribes the spatial and temporal evolution of mechanical hot spots remains elusive. Here, we introduce a geometric framework compatible with hierarchical representation of textiles built up from the yarn level to provide localized measures of curvature, area, and volumetric changes, providing predictive descriptors for the onset and migration of mechanical hot spots. The proposed framework is general and adaptable to a wide range of flexible systems, from weaves and braids to polymers and architected entangled networks. By bridging geometry with continuum-scale mechanical insights, this approach advances a systematic quantitative description of geometric nonlinearity and enables design principles for flexible systems.