Well this sounds like you are doing a science fair project and you want to find out under what conditions fresh cut flowers stay fresh for the longest time.
I would not only think of putting different chemicals into the water but also look at different room temperatures, and different pH of the water. And make sure you have a control (where you put nothing at all into the water).
You should also compare your experiments with fresh flowers that have some of the powder in it that helps flowers to stay fresh and that you can buy at stores. Maybe on the back of the package it tells you what chemical they use. Most often there are salts (nitrates) in it and something that keeps bacteria from growing. It don't know where you could get these chemicals yourself unless your high school chemistry department has them. If you live in a University town you could see if you could find a chemistry lab that can help you.

If you cannot get any chemicals I would try some different approaches. Maybe you can see if putting a copper wire or other metals have an effect (I have read somewhere that silver does) or maybe adding a little alcohol (rubbing alcohol for example) to the water will do the trick. I also mentioned temperature and pH of the water. You can add plant fertilizer which you can by in stores or do a mixture of all of the above. Just make sure you always compare it to a sample with nothing added to the water and with a store bought product added to the water. This give you an idea if you are creating something better or not.
Try something out of the ordinary too, maybe it works.