Effects of the rheological properties of non-Newtonian middle fluids on the formation dynamics of double emulsions in coflowing microfluidic emulsification are systematically ascertained by both experimental investigation and numerical simulation with a volume of fluid-continuum surface force model. In the experiments, with non-Newtonian fluids as the middle fluids for the generation of double emulsions, six various flow regimes, including dripping, jetting, transition, nonbreakup, parallel, and multicore regimes, are distinguished, and the corresponding formation mechanisms of such distinct flow regimes are further comprehensively revealed by analyzing the flow field structures and viscosity distributions inside the double emulsions. Particularly, a large flow velocity of the outer fluid only contributes to the generation of a transition regime but not a jetting regime because of the shear-thinning property of the non-Newtonian middle fluid. The regimes in the flow pattern diagrams dependent on the capillary number of the outer fluid, the Weisenberg number of the middle fluid, and the Reynolds number of the inner fluid are obtained. Besides, the size variation laws of double emulsions under various operation conditions are also illustrated. As the flow velocity of the middle fluid increases, the inner diameter of the resultant double emulsions remains constant within a specific range because the increase of the flow velocity always results in the decrease of the middle fluid viscosity, thus determining the nearly invariant viscous shearing force acting on the inner fluid. Finally, the prediction correlations for the dimensionless inner and outer diameters of double emulsions with several key dimensionless numbers are established, and the prediction errors are within ±10%. The results of this study provide valuable guidance for the preparation of monodisperse double emulsions with non-Newtonian fluids as the middle fluids in a controllable and precise manner.