We use Brownian dynamics simulations to study the topological simplification of knots that untie from chains in elongational flows. Focusing on the 81 knot, we track changes in conformational states as initially centered knots move off chains in planar elongational flows. We show that the non-uniform tension profile along the chain leads to a redistribution of conformational states at different knot locations along the chain. The rotational mode of motion for knots in elongational flows promotes a preferred knot conformational state rearrangement pathway, which results in a dominant untying pathway. The interplay between chain tension, conformational state rearrangement pathway and knot untying time is further probed by varying chain length. Finally, we generalize our findings by considering the untying pathways of other twist knots in elongational flows. From a practical standpoint, using flow kinematics to influence the topological simplification pathway of a knot can be potentially exciting for single-molecule applications.