If you put petroleum jelly on the petals of a living rose, you will kill the flower. Plants and flowers like roses need three things to live: water, sunlight and carbon dioxide. Petroleum jelly creates a seal that does not allow either water or air to pass through, and inhibits sunlight. The petals will not be able to drink or breathe. Water vapor will be trapped in the petals and the petals will suffocate. Imagine if you coated yourself in petroleum jelly, including your nose and mouth. You would not be able to drink or breathe. This is the same effect the flower would suffer if you coated its petals.
Petroleum jelly might be bad for living roses, but it is good for preserving dead ones. Coating rose petals in petroleum jelly will prevent them from decaying. Coating a rose petal in petroleum jelly would have the same effect as coating a wound or burn; the petal would be protected from germs and other microorganisms that might want to eat the petal. Thus, the petal would not decompose. The petroleum jelly will cause the rose petal to wilt, however. That is because when the petal is coated in petroleum jelly, the water already in the petal is trapped inside. The dead petal can no longer transpire or release water vapor, and in turn will turn mushy.
You can mix rose petals with petroleum jelly when you are making beauty products. These days, most petroleum jelly is used for cosmetic purposes. Petroleum jelly preserves the moisture in your skin, but it does not smell great. When you mix petroleum jelly with rose petals, you can enjoy the benefits of both substances together. The petroleum jelly will make your skin and cuticles soft, and the rose petals will make them smell pleasant. Petroleum jelly can even preserve the scent of rose petals long after they are dead.