Despite recent advances in Rectified Flow Models (RFMs), unlocking their full potential for controlled generation tasks—such as inverse problems and image editing—remains a significant hurdle. Although RFMs and Diffusion Models (DMs) represent state-of-the-art approaches in generative modeling, their reliance on computationally demanding backpropagation through ODE solvers and inversion strategies often undermines efficiency and precision. In this paper, we present FlowChef, a novel training, inversion, and gradient-free inference-time steering strategy for RFMs that deterministically guides the denoising process. We first develop a theoretical and empirical understanding of the vector-field dynamics of RFMs in efficiently guiding the denoising trajectory. Specifically, leveraging the straightness and smooth Jacobian properties, we derive the mathematical relationship between gradients of rectified flow ODEs. We extend our theoretical findings to solve linear-inverse problems, image editing, classifier guidance, and many more tasks. We perform extensive evaluations and show that FlowChef significantly exceeds baselines in terms of performance, memory, and time requirements, achieving new state-of-the-art results. Remarkably, for the first time, it scales effortlessly to billion-parameter models such as Flux. We release code and demos at: https://anonymous.4open.science/r/FlowChef/