The sensitivity to the vaporization Damkohler number of the behavior of a co-flow laminar spray diffusion flame in an oscillating flow field is investigated. Droplet grouping induced by the host gas flow oscillations is accounted for. The spray is modeled using the sectional approach and a perturbation analysis using a small sectional Stokes number is utilized for solving the liquid phase governing equations. The effect of droplet grouping is described through a specially constructed model for the vaporization Damkohler number that responds to the proximity of the droplets as they cluster due to the spray-flow oscillations. A formal analytical solution is developed for Schwab-Zeldovitch parameters through which the dynamics of the spray flame front shapes and thermal fields are deduced. Computed results based on the solutions demonstrate how strongly the vaporization Damkohler number including droplet grouping effects impacts on the type of primary homogeneous flame formed and on the possible existence of multiple flame sheets as a result of dynamic changes from under-to over-ventilated flames as the flow field oscillates. A further subtle, allied phenomenon that produces isolated regions of high fuel vapor concentrations is fuel droplet enrichment that stems from the combination of droplet grouping and the oscillating droplet and host gas flow fields. Such regions also lead to the formation of multiple flames under certain operating conditions.