If you put the food coloring on the flower it will turn that color. However if you put the food coloring in water and place the flower in that water, the flower gradually absorbs the color. It has a nice effect and is readily experimented for elementary science projects.
If you put white Carnations in colored water. They should turn that color. When you put them in; cut the stem at a slant so it easier for the flower to slur up the water. It takes a little while for the change to occur but if you use the right amount of coloring in the water they should turn out beautiful.