Molecular architecture plays a key role in determining the physical properties and emergent functional properties of polymeric materials. Despite recent progress in the synthesis of structurally defined polymers, we still lack a complete understanding of how the emergent properties of topologically complex polymers arise from molecular-scale phenomena. In this work, we study the nonequilibrium dynamics of DNA-based comb polymers in extensional flow using a combination of single molecule fluorescence microscopy and Brownian dynamics (BD) simulations. In this way, we directly observe the stretching dynamics of single DNA comb polymers in planar extensional flow. Transient stretching dynamics of isolated comb polymers is studied as a function of branch density and location, branch molecular weight, and flow strength. High-fidelity BD simulations are used to provide a direct complement to single molecule experiments, providing key insights into the molecular stretching mechanisms for single combs in flow. Our results show that comb polymers stretch through fundamentally different conformational pathways compared to linear polymers. In particular, comb polymers exhibit hindered transient stretching in extensional flow, which arises due to nonlinear chain topologies. From a broad perspective, this work provides a molecular-based understanding of topologically complex polymers in flow, which could aid in the modeling and processing of advanced polymeric materials with nonlinear topologies.