Many kids (and adults) struggle with anxiety when traveling by plane. My son, now 10, would become very anxious whenever we got to an airport or boarded a plane when he was younger (he's been traveling by plane at least once a year since he was 10 months old), even though he has always been interested in and fascinated by planes. The last few years, he's become much more able to deal with that anxiety, and his fears have subsided somewhat, but he is still not a completely relaxed air-traveler.
I think that one of the best ways a parent can help an anxious child, is first of all to be prepared for the anxiety so that any "outbreaks" do not catch you off-guard. Being prepared makes it easier to stay calm, and in turn easier to help your child calm down.
Here are some of my thoughts and tips about seven situations during your trip that can potentially trigger problems for a child that is anxious about flying. These are all trouble-spots that I've had personal experience with when traveling with my own children.
1. Parting with your luggage at check-in
To an adult, this might not seem like a very big deal at all: put your suitcase on the conveyor, then pick it up at your destination. For a child, who might not yet know the particulars of how luggage is handled on a flight, this can be a very big problem. My son would sometimes cry, cling to the suitcases and refuse to let go of them at check-in. Part of the reason why was that he was worried he'd never see those bags again.
To make this step easier, prepare your child ahead of time. Tell them that your luggage will go on the same plane, and will arrive at the same place as you do (then hope it does not get lost in transit...). Also, letting your child help put some name-tags on the suitcases, and help you put the luggage on the conveyor, might also help.
2. Going through security
Going through security can be a stressful experience for all travelers. There are often lineups , and you might have to remove shoes or other items of clothing. My kids are sometimes a bit reluctant and fearful of going through the metal detector on their own. If there are two adults traveling with the children, it does help if one of them goes through first. If you're traveling on your own (as I have done on several occasions), you might have to gently push them ahead of you, and hope the staff at the metal detector are helpful and encouraging.
Another problem for kids can be that they find it difficult to part with their carry-on, including any safety blankets and stuffed animals they've brought, and put their belongings through the x-ray machine. Both my kids have had minor or major panic attacks at security for this reason. Explaining exactly what is going to happen before you get to the x-ray machine and metal detector usually helps reduce those fears.
3. Getting settled in your seat
This was one of the biggest flash-points for trouble when my son was younger. Sitting by himself (rather than on my lap) and putting on a seat-belt he didn't necessarily want to put on, would often cause him severe fear and anxiety. On one flight, he refused to put his seat-belt on so loudly and strenuously that I feared we'd end up delaying the flight.
What worked for my son was mainly just experience: as he got older and more used to flying this anxiety subsided. In the moment, when he was almost terror-struck, what worked was basically just to hold him as best I could, hug him and quietly talk to him to reassure him. Occasionally I would have to strap on his seat-belt while he was still very fearful, and those were not feel-good parenting moments, but holding him close as he sat next to me, and leaning over to comfort him did help us both.
As always: talking about what is going to happen and why ("you need your seat-belt to be safe") ahead of time is helpful both in the short-term and long-term.
There are a lot of strange stuff going on during take-off: loud engine noises, bumps on the runway, air rushing around the plane as it climbs, changes in air pressure, and so on. If your child is scared of flying (and even if they're not usually frightened), it can be a rather intense and scary experience. My daughter, who is not that scared of being on a plane in general, sometimes holds my hand very tightly and hides her face in my shirt during take-off.
Be prepared for this. Hold your child. Talk about what the different noises are and what is happening: "We're going out on the runway. We're waiting our turn. The engines are starting up" And so on. Reading about airplanes and airplane noises before your trip can also help.
Just like during take-off, there is a lot going on when the plane starts to descend. Wings change shape, the landing gear thumps as it comes out, engine noises increase, and the change in air pressure often becomes really noticeable. All of this can be extremely stressful for a child, especially an anxious one.
Be ready for this. Talk to your child about what is happening and what is making all those noises. Hold their hand, and hug and comfort them as best you can while you both remained strapped in. Being ready with a favourite comfort-item like a stuffed animal or blanket can also help. Chewing gum, sucking on a pacifier or bottle (or maybe a lollipop), can help with the ear-pressure.
I think pretty much everyone that travels on a plane gets at least a little nervous when there's turbulence during the flight. I know both of my kids do. To help them, I try to stay calm myself, and explain why the turbulence is happening. Even a simple explanation like: "It's just some bumpy air, just like a bumpy street", seems to help at least a little bit. Other than that, it's just hugs and hand-holding.
7. Getting off the plane
The mad crush of passengers getting out of their seats and standing up in the aisle waiting for the airplane doors to open can cause real stress and anxiety for kids. Children might be very impatient to get off the plane, and might not understand clearly why they can't do so. If you can, and you're not in a big hurry for a connecting flight, then try to remain seated until most people have cleared out of the plane. That doesn't always work with eager kids (like mine).
The main thing I've found that calms my own children down in this situation is once again to talk about what is happening and why. I explain that the crew is waiting until everything is ready for the passengers to get off the plane, that doors must be opened, maybe stairs have to be brought over, and so on.
To reduce stress and anxiety when you're disembarking, it also helps if you've taken your kids to the bathroom before the plane lands. Otherwise, the moment when everyone is standing up waiting to get off the plane, seems to be when my children suddenly REALLY need to go, and then it's pretty much impossible to get to a bathroom.