Our kids (now 9 & 10) have been flying fairly often since they were about 3 months old. By often they do perhaps 8 - 10 flights a year on average.
I don't understand this 'burning off energy bit' and I can't understand why kids should become a total pain in the jacksie for other passengers just because the kids can't sit down & be reasonably quiet for a few hours. And I and the wife are hardly strict disciplinarian type parents.
For a start - the bigger deal the parents make of the flight the more th' kids will think it's a big deal and act accordingly. Make out it's perfectly normal and matter of fact and they'll pick up that this isn't an opportunity to create drama.
That said the kids can be encouraged to look forward to something that they should very much enjoy and take interest in. Nowadays most flights over a couple of hours are going to have some kind of IFE so if your children can't keep still and quiet for 90 odd minutes you may want to reconsider taking any public transport.
The only time we had any problem with one of our kids the couple in the seats behind were trying to tease and play with our toddler daughter and trying to feed her chocolate. Quite honestly relying on feeding kids candies to keep them quiet isn't a good idea and when our daughter had had enough chocolate and enough teasing she was sick. So running around and eating isn't a great idea.
Before the flight - if your kids are old enough - show them the airport and show them what planes look like taking off and landing and just taxing around - if they aren't used to it it's fascinating. I'm 41 - it fascinates me. You don't need to feed them up, starve them or have them work out in the gym to get tired - nor do they need valium or methamphetimines. Act like it's a normal day and feed them accordingly.
If possible get them a seat with a window and an aisle. They (if there is more than one delightful little snowflake) can take turns to sit by the window - strangely enough most of them love looking outside. If you haven't filled their heads with ideas that the plane will fall out of the sky mostly they won't be remotely concerned.
Really little kids need stuff to keep them occupied. Keep the chocolates for grandma and try to give the kids things that take them ages to work out - opening in-flight cutlery packs can keep them amused for a while as can working out how to use the IFE controls - when the kids have worked it out they can show you - it'll save you time and heartache and you might get to watch a film all the way through.
After they've watched out of the windows, read books, played with the kid toys give away packs, eaten food, watched films and videos, eaten 'treats', drank pop, gone to the toilet a dozen times, played with surprise toys, ran around playing hide an seek, kicked the back of the seats in front, pulled the head rest back a few times and puked up they might be tired - let them go to sleep. Please.