When the sky looks blue, it is due to the weak scattering of blue light by and within the atmosphere, due to an effect called Rayleigh scattering.
Effectively, air is slightly reflective of blue light.
When the sky (or clouds) look red, it is because most of the blue light has been reflected away along that line of sight, again due to Rayleigh scattering, leaving the red light to arrive relatively unobstructed to your eye from brightly lit white objects (eg clouds).
To a lesser degree than the red, but more so than the blue, green light will also arrive along the line of sight from bright objects. When green and red arrive together, the human eye registers it as yellow. If you doubt this, you need only examine a color tv screen up close in a yellow area to see that it is actually composed of tiny interleaved dots of green and red.
Similarly, to a lesser degree than the blue, but more so than the red, green light will also be scattered by the atmosphere. When blue and green light arrive together, the human eye registers it as turquoise. Again, look at a tv screen up close.
At points in the sky in between the red and blue colors, some green light will be present, but the points will appear either yellow or turquoise, depending on whether there is more red or more blue light mixing with it. When the blue and red are equal, the green will still be less than either, since green scattering is weaker than blue and green transmission is weaker than red. At these points, the sky could look pink or lavender.Thus you can never find a spot in the sky which looks purely green.