We present and solve the dynamics of a model for gene duplication showing escape from adaptive conflict. We use the Crow-Kimura quasi-species model of evolution where the fitness landscape is a function of Hamming distances from two reference sequences, which are assumed to optimize two different gene functions, to describe the dynamics of a mixed population of individuals with single and double copies of a pleiotropic gene. By mapping the evolutionary dynamics onto the dynamics of a quantum spin chain, we derive the spin coherent state path integral  representation and solve the evolutionary dynamics equation under saddle-point semiclassical approximation. The linear fitness landscape with two reference sequences is analyzed to show phase diagrams on the mutation-fitness parameter space. More importantly, we focus on the dynamics of a population escaping adaptive conflict through gene duplication and calculate the time scale at which the duplicated genes start to dominate in the population. We also show that there is an optimum mutation rate which minimizes this time scale.