Why does salt prolong the life of cut flowers the longest?

it most like wasn't the just the sugar that maintained the flower, but its concentration in the water. the solute concentration (sugar) in the water was probably equal, or close to equal, to the solute concentration in the cells of the flower. this would establish an osmotic equilibrium that satisfied the maintainance of the cells for an extended period of time. you'll want to try repeating this experiment with varying concentrations of sugar for each flower. the same is true for all of the solutions you used: vinegar, which contains no water would have drained the flower of water. the solutions that contained water would easily have lasted longer than the vinegar by the same principle that a kind of temporary osmotic equilibrium would be established allowing those flowers to live longer