Sounds like a fun project to see capillary action!So, why did just the outer edges change color? Why not all the petals?
There may be a couple of reasons for this. Think of the flower as a straw from the bottom of the stem to the tip of the petals. Using capillary action, the plant keeps drinking up the dyed water until it's brought up all the way to the tip of the petals just like when we drink through a straw. Now, if the flower can still drink the water up or if there is enough dye, it should be able to transform the entire flower into the color of the dye. If the flower couldn't drink up the water after 72 hours, you can help it.
Because the flower no longer has a root system, the stem needs to be kept well-maintained and fresh to keep being able to drink up the water. You'll need to have an adult help you cut the tip off a little bit at an angle every other day to help the stem "drink" up the dyed water, use cool water, and change the water every day or every other day to keep it drawing up the dye. It could also be that the concentration of the dye is too little at the original or two times the amount--what happens if you try 4 times or 8 times? The dye doesn't damage the flower, so try it and see
The outer edges dry out first?
Just as humans can become dehydrated through sweating, flower petals will dry out from transpiration if they do not have a source of fresh water. Petals are covered with minuscule openings called stomata through which water evaporates, so the lost water needs to be replaced for the plant to stay healthy. Flower stems draw water up from the roots to the petals through a series of channels, or tubes, named the xylem. Cut flowers placed in water continue to draw water up through the xylem to keep the leaves and flower petals well hydrated. As water droplets leave the stomata, they are replenished.
Remember the straw concept? Well, it kind of works the opposite way too. You'll see this happen too during the fall season when trees suck back their chlorophyll into their roots and trunk to store it for the winter--which is why tree leaves change colors and eventually brown and fall off. It's the same thing for flowers. In the case of a cut flower instead of a planted one, when it starts to wilt, it draws water from the tip and back down to the stem to keep the flower's stem moist.
Here is a great website from the Missouri Botanical Garden to help you learn more about plants: http://www.mbgnet.net/bioplants/parts.html
You can find a good explanation about capillary action here: http://www.uni.edu/~iowawet/H2OProperties.html
Hope this helps! Good luck with your project