To investigate parsec-scale jet flow conditions during GeV γ-ray flares detected by the Fermi Large Angle Telescope, we obtained centimeter-band total flux density and linear polarization monitoring observations from 2009.5 through 2012.5 with the 26 m Michigan radio telescope for a sample of core-dominated blazars. We use these data to constrain radiative transfer simulations incorporating propagating shocks oriented at an arbitrary angle to the flow direction in order to set limits on the jet flow and shock parameters during flares temporally associated with γ-ray flares in 0420-014, OJ 287, and 1156+295; these active galactic nuclei exhibited the expected signature of shocks in the linear polarization data. Both the number of shocks comprising an individual radio outburst (3 and 4) and the range of the compression ratios of the individual shocks (0.5-0.8) are similar in all three sources; the shocks are found to be forward-moving with respect to the flow. While simulations incorporating transverse shocks provide good fits for 0420-014 and 1156+295, oblique shocks are required for modeling the OJ 287 outburst, and an unusually low value of the low-energy cutoff of the radiating particles' energy distribution is also identified. Our derived viewing angles and shock speeds are consistent with independent Very Long Baseline Array results. While a random component dominates the jet magnetic field, as evidenced by the low fractional linear polarization, to reproduce the observed spectral character requires that a significant fraction of the magnetic field energy is in an ordered axial component. Both straight and low pitch angle helical field lines are viable scenarios.