After purchasing your flowers, re-cut the stems and remove all of the excess foliage, so they can absorb the extra moisture and food they'll need for travel.
Mix floral preservative in a vase with warm water. Place the flowers in the vase and set it in a cool place. Allow the flowers to "harden," maximizing their absorption of the warm water and food as the water cools to room temperature.
Wrap the flower stems in paper towels soaked in the (now room temperature) water from the vase. Wrap a thick plastic bag around the paper towels and secure it around the top with a rubber band.
Line an insulated box with a towel. Place the flowers inside. Add a small ice pack to keep things cool inside the box.
During the flight, ask the attendant on board if she could place the flowers in water back at the attendants' station.
