I've done this very experiment with my Kindergartener and daisies. We used both red and blue food coloring which filtered up the stem and out into the white petals. It was a really neat transformation.
Food coloring will affect the plant bloom by changing the color of the bloom to the same color as the food coloring. As the above poster noted try this with the Queen Annes Lace to see the changes.
If you put a plant’s stem (or roots) in food coloring, the colored water will be drawn up through the root or stem system, and the bloom will be tinged with whatever coloring the food coloring is. Try this with the lovely weed—Queen Anne’s Lace. The change is not fast, and it’s not dramatic, but it is noticeable.
I've also completed this experiment with the students in my class except we used celery that still had some of the leaves at the top. It is really interesting to cut the bottom of the celery in half and put one side in one cup of food colouring and the other side in another cup of food colouring. I find sometimes red food colouring damages the plant, as some red food colourings are not so great for you.