I'm going out on a limb here, but I'm assuming that blue and yellow are the colors because of the power each holds to the mind.
Blue, particularly light blue, is a color that spreads happiness among people. The waters of Hawaii, and other tropical areas with light blue crystal waters, greatly increases happiness and contentedness among people through chemicals in the mind. Its a most 'beautiful' color (one of my favorite colors) and it shows dependability. In the case of Downs Syndrome, it shows the people involved in it are committed and dependable.
The color yellow also evokes happiness, and creates a feeling of energetic quality in the body and mind, as well as an optimistic view.
When the yellow is mixed with the blue, it shows a mix of dependability and perseverance with optimism and a bright future ahead of these people with Down Syndrome with their help and support, and hopefully ours.