At sunset the cumulative effect is to 'elevate' the sun's image by about half a degree above its true position. The naked eye's resolution limit is only about 120 seconds of arc, which explains why we don't normally see a blue fringe at the top of the sun and a red fringe at the bottom. The top of the sun's 'red disk' is tangent to the horizon and is setting normal to it. In 1.4 seconds the sun's 'blue disk' will sweep towards the horizon and vanish. During that time you will see light that has progressively more colours subtracted from it, first red, then orange, then yellow, etc., until in the last split second before the sun totally disappears there should only be blue.
Some people do.
Lord Kelvin, in 1899, referred to exactly that when he described the sun rising over Mont Blanc, Switzerland. But there are good reasons why the flash should usually be green, and not blue. The light sensitivity of the human eye is a function of wavelength. The scarcity of blue light causes the peak stimulus to shift slightly towards the yellow, making a blue flash less likely and a greenish-yellow one more likely. A blue flash can occur only if the atmosphere is unusually clear, and scattering does not deplete the sunlight of too much of its blue component.