1. Bring a large pillow. When we flew to the US with our 15 month old we bought two tickets. On two flights (China to LA) and (WAS to Abu Dhabi) we got lucky and had an empty seat so that was super. On two flights (SR to China, and Abu Dhabi to BKK) we didn't get so lucky. But the pillow allowed us to have him sleep on our laps.
2. thin blanket you don't care about. Something is going to go wrong and a big mess will need to be absorbed!
3. Lots of wipes & diapers. And a couple of cheap washcloths that you can use to wipe him down during the flight if needed.
4. formula. We brought a brand new (unopened) small sized can. AND we had put formula into 4 bottles we had in our carry on. That way we didn't have to open the can until the 2nd flight and went through security with the can unopened. Our experiences flying have been ok, but I've read that it can be hit/miss as it pertains to open baby formula.
5. Can of snacks - we had a gerber cheese curl type thing. More for the layovers than the flights.
6. Brought one toy for the layover - small car that he could push around. On the plane he joked with other passengers behind us, watched cartoons on the tv, and looked at videos we had loaded on my wife's phone (and we had bought/used a portable phone charger that my wife brought - allowed us to recharge the phone twice during the trip without needing a plug). And he slept a lot.
7. two change of clothes (in China there was a baby changing room and we used it to give him a quick bath and put on fresh clothes) - I had actually thought ahead and brought an empty water bottle from the plane and we used that to give him a bath/shower. And a change of clothes for yourselves! I had to change a shirt when a food tray got flipped over by my son
8. Stroller. Flying from SR to US we went through China - had to literally refuse to get on the bus from the plane as they kept telling me to go to baggage claim to get our stroller (well we weren't going to baggage claim as we were transit passengers!!!). Finally, they relented and gave us the stroller - if we weren't able to point to it across the plane I think we would have lost it. When we flew back - they wouldn't gait check the stroller for Abu Dhabi - they said there were loaners we could use (in Abu Dhabi that was true - but not in BKK). So that was messed up - we used the small baggage strollers that are around the airport in BKK as our stroller when we transferred in BKK.
9. We were flying as a family so both mother and father were present. If thats not the case, you'll need a certified letter from the other spouse saying its ok for the child to travel AND you should have a copy of the birth certificate just to be on the safe side. When arriving in the US the one difficult thing was I had to scan my son's passport and then hold him up for his photo - it was tricky and took three tries. There was no sign of any priority line for those with babies that I saw - though in fairness the line we were in only took about 15 minutes to get to the machines. Surprisingly I wasn't asked about his mother (who was on the other side with her visa) by the immigration officer - was basically - welcome home. On a previous trip - arriving in Bangkok we were escorted to the front of an immigration line due to having a baby but that didn't happen in LA.
It was not my son's first flight - he had flown twice before to/from Bangkok and he enjoyed those flights. Overall it was ok. My wife was pregnant at the time so it was a long trip for her but we managed ok. We did not give him anything in terms of medicine nor would I consider doing so. We simply kept him engaged until tired and let him sleep.
One final note - my son flew out of Cambodia using his Cambodian passport at immigration (which had his exit card from our previous trip), entered the US on his US passport (when we checked in we presented his US passport to airline so they know he can enter US - did reverse when flying from US - showed Cambodia passport). When we arrived back in Cambodia the guy literally couldn't understand how our son didn't have a US stamp in his Cambodia passport. He didn't allow me to be up with my wife/son during the process - he then asked my wife where they flew in from - she said Bangkok. He then went bizerk claiming that we were doing something wrong - a manager/more senior person was called - I ignored their instructions to stay back and simply took the passports from the 1st guy and explained to the 2nd guy what was done (and that we were never "in" Bangkok - just transiting). They then both claimed that this wasn't ok - that he needed to use his US passport or he needed stamps in his Cambodia passport from Thailand and US - I simply refused to do that and told them they were incorrect. Finally another gentleman appeared - explained the situation to him and he said ok. I told my wife next time we're picking a line with a younger person or woman. Those two guys weren't the sharpest tools in the shed.
Good luck with your trip.