Magnetohydrodynamic (MHD) plasma turbulence is believed to play a vital role in the production of energetic electrons during solar flares and the non-thermal broadening of spectral lines is a key sign of this turbulence. Here, we determine how flare turbulence evolves in time and space using spectral profiles of Fe xxiv, Fe xxiii and Fe xvi, observed by Hinode/EIS. Maps of non-thermal velocity are created for times covering the X-ray rise, peak, and decay. For the first time, the creation of kinetic energy density maps reveal where energy is available for energization, suggesting that similar levels of energy may be available to heat and/or accelerate electrons in large regions of the flare. We find that turbulence is distributed throughout the entire flare; often greatest in the coronal loop tops, and decaying at different rates at different locations. For hotter ions (Fe xxiv and Fe xxiii), the non-thermal velocity decreases as the flare evolves and during/after the X-ray peak shows a clear spatial variation decreasing linearly from the loop apex towards the ribbon. For the cooler ion (Fe xvi), the non-thermal velocity remains relativity constant throughout the flare, but steeply increases in one region corresponding to the southern ribbon, peaking just prior to the peak in hard X-rays before declining. The results suggest turbulence has a more complex temporal and spatial structure than previously assumed, while newly introduced turbulent kinetic energy maps show the availability of the energy and identify important spatial inhomogeneities in the macroscopic plasma motions leading to turbulence.