Kinetic models of metabolic networks relate metabolic fluxes, metabolite concentrations, and enzyme levels through well-defined mechanistic relations rendering them an essential tool for systems biology studies aiming to capture and understand the behavior of living organisms. However, due to the lack of information about the kinetic properties of enzymes and the uncertainties associated with available experimental data, traditional kinetic modeling approaches often yield only a few or no kinetic models with desirable dynamical properties making the computational analysis unreliable and computationally inefficient. We present REKINDLE (REconstruction of KINetic models using Deep LEarning), a deep-learning-based framework for efficiently generating large-scale kinetic models with dynamic properties matching the ones observed in living organisms. We showcase REKINDLE's efficiency and capabilities through three studies where we: (i) generate large populations of kinetic models that allow reliable in silico testing of hypotheses and systems biology designs, (ii) navigate the phenotypic space by leveraging the transfer learning capability of generative adversarial networks, demonstrating that the generators trained for one physiology can be fine-tuned for another physiology using a low amount of data, and (iii) expand upon existing datasets, making them amenable to thorough computational biology and data-science analyses. The results show that data-driven neural networks assimilate implicit kinetic knowledge and structure of metabolic networks and generate novel kinetic models with tailored properties and statistical diversity. We anticipate that our framework will advance our understanding of metabolism and accelerate future research in health, biotechnology, and systems and synthetic biology. REKINDLE is available as an open-access tool.