With little sunlight and turbulence, airline flights are not the friendliest places for plants. You can keep flowers looking as fresh as when you bought them, even after a several-hour flight, if you take several measures. Many of the measures that can be taken to preserve flowers during the flight are the same measures that are taken to preserve flowers in general.
Remove unneeded foliage and cut the stems of the flowers.
Fill a vase with warm water and the flowers. Place the vase in a location where the flowers won't dry up due to the sun. Warm water will absorb into the flowers much more quickly.
Treat the flowers in the vase with preservatives. Lemon lime soda can be substituted as a preservative if your fresh flowers did not come with a preservative packet.
Cool down the water from the vase to an average temperature and soak some paper towels in the water. Extract the flowers from the vase and wrap them in the paper towels.
Wrap the flowers again with a thick plastic bag to prevent moisture from escaping.
Tighten the plastic bag with several rubber bands. Do not damage the flowers with the rubber bands.
Place an ice pack in a rigid, plastic box. Place the wrapped flowers in the box. This is especially important for long flights.