We describe the dynamics of an isolated, flexible polymer molecule in an extension-dominated planar mixed flow. We find that as vorticity is added to planar extensional flow, the conformational fluctuations of the molecule increase and the coil-stretch hysteresis [e.g., Schroeder et al., Macromolecules 37(24), 9242 (2004); Science 301, 1515 (2003)] vanishes for a fixed Deborah number and Hencky strain. We present Brownian dynamics simulation results and a kinetic theory, valid in the hysteretic regime, which allows us to determine both the rate at which a coiled molecule unravels and the rate at which a stretched molecule relaxes to a coil when subjected to planar mixed flow. We demonstrate that for all values of the added vorticity, the coil-stretch/ stretch-coil transition rates increase with increasing vorticity as a consequence of the conformational fluctuations, which can be explained by the molecule sampling a shear flow through Brownian fluctuations off the extensional axis. We demonstrate that if R-g vertical bar( root alpha L) << 1, where R-g is the radius of gyration, L is the molecular contour length, and a is the so-called ''mixedness'' parameter, the transition rate increase is explained in terms of an effective conformational diffusivity, which can be evaluated using a convective dispersion analysis. (c) 2007 The Society of Rheology.