The shear rheology of a model wormlike micellar solution exhibits moderate shear thinning and curved flow velocity profiles without discontinuity (nonbanding case). The shear rheology and the flow kinematics are analyzed within the framework of the Giesekus constitutive equation. Macroscopically, the steady state flow curve of the solution exhibits shear thinning with a shear exponent < 1 without hysteresis, indicative of a sample that does not shear band. The microstructure of the micellar network is probed by the combination of dynamic rheology, rheo-optics, and SANS. Flow kinematics in a Couette geometry are measured by particle tracking velocimetry and found to be consistent with predictions of the Giesekus constitutive equation fit to the bulk shear rheology. 1-2 plane SANS measurements of the segmental alignment under shear are also found to be in agreement with predictions of the constitutive equation, providing a coherent picture of the mechanisms by which wormlike micelles flow and shear thin. The degree of segmental alignment is found to lag behind predictions of the model, which is postulated to be a consequence of the long, branched topology of the wormlike micelles.