I've found that Manitou wasn't sufficiently prepared to fly just from routine downstay work on restaurants, etc.
Hearing dogs don't always know when to "turn it off" re sound alerting, and public transit is a big challenge for these dogs. On a bus, train, or airplane, there will be a lot of sounds similiar to or exactly the same as sounds that a hearing dog SHOULD alert to in other circumstances. The keener the dog is on sound work, the more confusing and frustrating corrections become, so it is really important to teach an "off" button. Restaurant work (which Manitou does fine with). wasn't enough for him to generalize to public transit, since there are more distractions.
I've been doing public transit training specifically-- teaching relaxed downs, do not break down whenever people get up, walk, or when doors open or close, and to ignore public annoucements, et cetera. On planes, there are many people (and dogs) moving out of sight, which for Manitou is particularly frustrating. There are also mechanical sounds, which interest Manitou (this dog let me know of car trouble twice.)
When I don't have access to live environments, I often Youtube videos with sound on full to help desensitivize my dog. I used this to help Manitou practice relaxing with baggage unloading and loading sounds, since they occur under the seats, which he found particularly disorienting. In a one-dog household, it is hard to causally train a dog on to the point they can ignore other dogs aboard for 3-4 hours, so this requires extra training effort, too.
The ability to squeeze and stay down in a tight spot is even more necessary now-- planes are continually getting more cramped. I pay for economy-plus seats now just so I can have Manitou walk into the aisle without crushing my knees, and he's light and narrow-- he's just tall enough his widest point is exactly where the narrowest point of plane seats are. He's also wriggled into dangerous spots with the bars underneath the seats which are designed to restrain luggage from sliding around, due to the increasingly cramped space.
Medication alone is not sufficient to calm a trained hearing dog, who often will wake up just to alert, and a half-groggy dog may be too wired to relax. Even tranquilizers can have risky side effects, especially on dog breeds more prone to breathing problems, and the dog may not be able to walk, either. Definitely do not try to short-circuit training gaps (or temperament issues) with drugs.
Now that we've addressed the training issues particular to hearing dogs, here's what flying with a service dog is like in general.
First of all, when booking look at both total time in air and the layover time. Plan for plane delays and if you do not have nonstop flights, make sure the layover is sufficient. I usually plan at least 3 1/2 hours so I can relieve my dog as needed, even if a plane is a hour late or more.
Once the flight's booked, it's best to notify the airlines at least three days in advance of your disability and needs-- they'll need to know how big your service dog is and how to accommodate your needs.
Usually at airports, the doggy relief areas are outside, and the exit will be by the baggage claims. You unfortunately have to go back in the airport through security, so I have to allow for at least 1 1/2 hours in a large airport just to get there, back through security, etc.
MSP has introduced indoors doggy relief areas, but these are just bare bathrooms with pee pads-- best for small dogs that are paper trained. I've never managed to persuade my large dogs to use them. I dearly wish that airports would just do outdoors courtyards with fresh air, gravel and wood chips, and room to roam.
If you do road trips with your dog you should already have a fair idea of how he deals with traveling, etc. when it comes to food/water. Do all basic grooming (nails, baths, monthly meds, etc.) before you fly out.
I now generally get a vet check around 10-15 days in advance of flying (at the earliest) to be sure he has his vaccine up to dates and certificates should it become necessary for emergency dog kenneling, and that also that he is perfectly healthy to fly.
If you are flying to a foreign country, be very aware of all the quarantine and laws governing flights and pet transport in these countries; you may have problems flying back with your dog if you do not have the paperwork, and some countries require a quarantine for dogs that arrive without complete paperwork (often required months in advance and dependent on the foreign country's bureaucracy to process properly.)
Generally, it is not worth the long flight, often crated (not in cabin) and added stress if you are flying out of country for a brief stay (less than a month). If you live in the E.U. you can get a pet passport that is good in all countries. I believe they may be applied for by non-EU pet dog owners, but it is not simple or cheap and this does not necessarily guarantee your dog will be able to fly under the host country's rules. It may be best to arrange a cruise, driving in, or other transport if you must keep your service dog with you.
When it comes to preparing your dog's hygenie for flying, here I'm going to re-parrot some of the standard wisdom I've heard over the years, which roughly is-- (depending on the source) to withhold heavy meals at least 12 hours before flying, no water at least 6 hours before, and and feed lightly just before flying and give small cups of water or ice chips in the air as needed. Relieve dogs thoroughly just before flying, of course.
This is intended to reduce the risk of accidents and help some dogs hold it through a whole 12 hour flight if needed, but I don't like having dogs hold it too long-- a full bladder left too long can raise risk of bladder cancer.
Definitely do not give lots of water until the flight is at least half done. You never do know if the flight will be delayed or rerouted. My old dog began refusing water altogether after he had a full bladder combined with a change in flight schedule and a re-route. He was hauling me the whole way to the doggy relief.
Next flight (which may be our last one together) I plan to ask ask very specifically that passengers be notified NOT to go pet my dog at all. The rise in therapy dogs in airports have made some people think my dog is a therapy dog to be petted without permission as soon as we board the plane, which does NOT help my training process at all.
Packing--I usually pack some of his gear in my carry-on, yes, including a day or two worth of dog food because flight delays do happen, and it's tough to get a special food right after landing if you come in late. Mostly, lots of poop bags. All heavy items go in the checked luggage.
Flying with a service dog's lots of work and added stress, really. I only do it because I need my dog with me at the destination and also to help handle some aspects of flying alone, not because I find it inherently fun.
I hope people who want to fly with their dogs in cabin will reconsider flying with their dogs when it's not necessary.