The coupling between the structure of the tilted condensed phases of docosanoic acid monolayers (L-2, L-2', and Ov) and an external shear flow has been studied using Brewster angle microscopy. Generally, the coupling results in a reorientation of the alkyl tails, although different kinematics are observed depending on the thermodynamic phase, shear rate, and surface pressure. The coupling can result in continuous orientational changes or in abrupt reorientation of the molecular tilt angle. These molecular-level effects are connected to the macroscopic texture as well; shear can result in either domain fragmentation or annealing. A detailed quantitative analysis of phenomena reminiscent of the "flow alignment" and "tumbling" mechanisms found in nematohydrodynamics is presented. The analysis reveals that the kinematics of the reorientation is different from that in nematic liquid crystals. The underlying lattice plays a crucial role, and the observed phenomena can be explained with geometrical arguments.