My brother is also afraid of flying.
I keep telling him that to think of it as a bus ride, and the bumps are just "dips in the road". If you don't look out the windows, you can actually feel thje similarity.
The take offs and landings are tougher to ignore, but if the person likes rollercoasters, that is quite similar.
Also, drinking may help, unless the person in question starts to loose it, then all bets are off.
Worse case scenario: imagine a fanatical drunk in an airplane?
(I haven't seen it, nor do I want to.)
Hopefully your calm reassurance will suffice. If not, mention that you did opt for the flight insurance because "you never know"!
I'm only kidding about the last part.
Simply bring an interesting book/magazine (On the water?), a walkman for inflight listening, and a few snacks (comfort food was named that for a reason.)
Good luck and enjoy your flight.