1st, pack lightly, try to have all of your carry on in the diaper bag. it's helpful if you choose a bad that can fit onto the stroller between the handle bars.
2nd, use an umbrella stroller. it might seem like a hassle, but after you carry baby for a mile, it gets tiresome.
3rd, does your baby do a binkie? he will need it on takeoff and landing. if not, feed him during these times as the cabin pressure changes, he will need to pop his ears.
4th, activities, i always flew the red eye with mine, even when i didn't she still slept. hopefully you get a window or isle seat, much easier for 'in and out' trips for diapers. it's also better so you can put baby in one arm, without accidently hitting your neighbor. take a spare bag or 2 for poopy diapers. bring a teething toy and another fav toy of his. my daughter loved it when i brought her 'snuggles' blanky. also snacks. graham crackers etc. you can take milk, but not water, they make you dump it out at security if it's water.
ALSO, do not put shoes on baby for flight, security makes them take em off. you should wear slip ons and no belt, otherwise you will be juggling. you will have to take him out of the stroller and sent it through the xray machine. both of your coats come off as well, so make them loose.
it's really easy, and most people love seeing babies, mine wasn't a cryer, hopefully yours isn't. good luck! let me know if this helped