When the beam of a flashlight travels through air, we cannot see the beam from the side because the air is uniform, and the light from the flashlight travels in a straight line. The same is true when the beam travels through water, as in this experiment. The water is uniform, and the beam travels in a straight line. However, if there should be some dust in the air or water, then we can catch a glimpse of the beam where the light is scattered by the edges of the dust particles. When you added milk to the water, you added many tiny particles to the water.
Milk contains many tiny particles of protein and fat suspended in water.
These particles scatter the light and make the beam of the flashlight visible from the side. Different colors of light are scattered by different amounts. Blue light is scattered much more than orange or red light. Because we see the scattered light from the side of the beam, and blue light is scattered more, the beam appears blue from the side. Because the orange and red light is scattered less, more orange and red light travels in a straight line from the flashlight.