We consider the problem of nonlinear rotating non-Newtonian jets in the presence of ambient flows. Using the original governing system of equations for such jet flows, we use scaling and perturbation techniques to reduce such system to a simplified one where the stress tensor is governed by Giesekus constitutive equations. We develop a method to take into account the effect of the ambient flow, which usually exists due to the externally imposed rotational constraint, on the formation of the non-Newtonian jet. We compute numerically the nonlinear steady solutions for the jet and determine expressions for the jet quantities like speed, stretching rate, radius, strain rate, and tensile force. These quantities are calculated for different values of the parameters such as those due to the ambient flow and viscoelasticity. We find that the ambient flow is stabilizing so that the strain rate, stretching rate, speed, and tensile force decrease with increase in the ambient flow effect, while the jet radius increases with such effect. The viscoelasticity of the fiber jet reduces notably the stabilizing effect of the ambient flow on the jet quantities, but the stabilizing effect of the ambient flow increases with the arc length of the jet centerline.