Flexural flow is thought unlikely to occur in naturally deformed, competent isotropic single-layers. In this study we discuss a particular case of folded bedding-parallel fibrous dolomite veins in shale, in which the internal strain pattern and microstructural deformation features provide new insights in the mechanisms enabling flexural flow folding. Strain in the pre-folding veins is accommodated by two main mechanisms: intracrystalline deformation by bending and intergranular deformation with bookshelf rotation of dolomite fibres. The initially orthogonal dolomite fibres allowed a reconstruction of the strain distribution across the folded veins. This analysis shows that the planar mechanical anisotropy created by the fibres causes the veins to approximate flexural flow. During folding, synkinematic veins overgrow the pre-folding fibrous dolomite veins. Microstructures and dolomite growth morphologies reflect growth during progressive fold evolution, with evidence for flexural slip at fold lock-up. Homogeneous flattening, as evidenced by disjunctive axial-planar cleavage, subsequently modified these folds from class 1B to 1C folds. Our study shows that the internal vein fabric has a first-order influence on folding kinematics. Moreover, the fibrous dolomite veins show high viscosity contrasts with the shale matrix, essential in creating transient permeability for subsequent mineralising stages in the later synkinematic veins during progressive folding.