I fly a lot on my own with my 4 and 1 year olds, and have done since they were tiny. My family live in Northern Ireland so I fly back and forth every few months.
I've found a few things have really helped make my life easier:
A ring sling - when I only had one child I used the ergo with no trouble, but when you're trying to settle two children in a poky plane, space is at a premium and the ergo is bulky! A ring sling doesn't even need to be taken off during the flight if you don't want, saving you struggling to take it on and off. It also can double as a scarf or a breastfeeding cover - super useful!
A travel wallet - I used an envelope to keep my ID and tickets together for ages, but I've just got a beautiful one from Kikki K which I adore, and which is even better than an envelope as it has a handy wrist strap!
Teething necklace - you knew I'd say that! But seriously they're so good. No metal bits to set off the metal detectors, keep you looking a bit stylish, baby in sling can fiddle with it or chew it, and doubles up as a toy when you're sitting on the plane.
Snacks. Snacks. Did I mention snacks? Preferably something that won't melt or mush, so no chocolate or fresh fruit. I don't usually have them but Ella's pouches are good for this situation, or dried fruit. Tuna sweet corn sandwiches - not so good. I will never forget the flight where my daughter was eating one and spat a mouthful into my hand. I had no free hand or any space to get rid of it so I just ate it. I now always make sure I have tissues ir wipes within easy reach when I'm on the plane.
Speaking of which, when you get on board, decant all that stuff into the seat pockets/your own pockets/a plastic bag hung from the arm rest, so everything is always handy. There isn't much space on board and if you've a baby on your lap it's difficult to reach things.
Hopefully this helps if you're flying solo soon! And if all else fails just go to your happy place and know it'll be over soon!