I used to be afraid of flying - but that was because I was on a flight where something bad happened that scared the crap out of me.
I got over it by earning a pilot’s license. This is, admittedly, a drastic approach and certainly not cheap. Nor is it particularly quick. So perhaps that is not the ideal approach.
Anyhow - you father should know that it’s actually quite common to be apprehensive or even fearful prior to a very first flight in an airplane. I’ve taken up first-timers several times and they are all a little scared… so really, some concern/fear means you’re normal.
I mean, really - we learn pretty early in life that falling down can hurt, and the further you fall the more it hurts. Remember learning to ride a bicycle, how you wobbled and feared falling down? Until you became confident the bicycle would hold you up, you had some anxiety. Likewise, until you becomes confident the airplane will safely get you from point A to point B you’re going to be a little concerned. Just normal anxiety.
You don’t understand how those big, heavy things stay up in the air, you don’t understand how they work, you don’t know what’s normal here. The motion is different, there are occassional alarming noises (things like landing gear going up and down), and you’re sitting jammed in a teeny seat next to people you don’t know for significant periods of time. My goodness, sometimes I think it’s a wonder anyone flies.
Anyhow, if your father could figure out what is making him so anxious it might help. Lack of control, perhaps? A lot of people are bothered by not being in control. In fact, it causes me problems on commercial flights - I’ve gotten real used to being in the cockpit, now they expect to trust strangers?. I just keep reminding myself that the guys up front have survived a very rigorous selection process in an extremely competitive career. If they weren’t good - nay, excellent - they wouldn’t be in front doing the flying.
Some people are bothered by the noises. Personally, since I have some idea what all the thuds and what not are I find them very reassuring. Those noises are the sound of things working. It’s like being afraid because a car door makes noise when you slam it - but if you’ve never been in a car before you aren’t expecting it, so it’s startling. Come to think of it, the sounds made by shutting the cabin doors can be intimidating - but again, that’s the sound of very solid machinery locking in your breathable air and locking out a hostile environment. I find thick, sealed doors reassuring. So is a good, solid sound of it locking.
Some people are bothered by being so high off the ground - this bothers my boss at work. So when I’m arranging travel for her I try to sit her in the center of the airplane, away from the windows she doesn’t want to look out of anyway. Me, I’m a touch claustrophobic (another reason I’m not fond of commercial air travel) so I do better if I can look out the windows - I’m still trapped in an aluminum tube, but I can look out which settles my nerves.
Don’t like bumpy rides? The smoothest ride is usually a seat over the wings (I try to get those for my boss, too.) Don’t like noise? Engines are either on the wings or, if not, at the tail - so rear seats may be noisier than those up front.
Everything just too new? Then a short flight might be in order… even on a turboprop. It will also give him something to compare the bigger airplane to, and I would expect the bigger plane would be much smoother and more pleasent a ride (I don’t know for sure - I’ve been in big jets and little dinky prop planes, but I’ve never been in a turboprop, oddly enough)
If you have a delicate stomach I’d recommend skipping on board meals entirely, if they’re even offered. Eat light prior to boarding, then eat again after arrival.
I’m not a big fan of sedation, however, if your father’s anxiety is excessive it might be worth talking to a doctor about it. It is an option. I do NOT recommend getting drunk - feeling ill on an airplane is not going to make you look forward to the next flight!
Anyhow, despite the normal concerns everyone has on their first flight, most people find it’s not too bad, and some folks wind up loving to travel quickly enough to put up with the aggravations of modern air travel. It is important, however, to make the first experience as pleasent as possible.
Wear comfortable clothes. Arrive at the airport early so you don’t have to rush.
Remember - modern air travel is the safest form of travel. Accidents are extremely rare. In many ways, it’s like taking a bus or subway, except the worst of the riffraff are filtered out by security before you get on board.
Also remember - fear doesn’t have to stop you. If you want to fly all you have to do is get on the airplane, even if you’re afraid. The cabin crew are used to nervous fliers - there are some on every flight - and may well have a word or two of reassurance. Remember, these people fly for a living. If they aren’t afraid you shouldn’t be, either.
Check back in if your father gets any insight to why he’s afraid.