I would recommend getting pre-mixed formula--that is sealed (you can buy Enfamil like this--in pre-mixed containers--and probably other formulas as well)--this will save you at lot of trouble at security--security checkpoints in Seoul and Tokyo and definitely in the USA are very thorough and they will make you unpack any baby food or liquids in your cases which can be a pain when you're handling a baby.
I just flew back from the States in mid-November with a 1-year-old, all by myself. It's a lot to handle with all the things you need on the flight for a baby. (Bags, stroller, baby, your own things etc.)
Security will not let you carry water on the plane--even though it's sealed--you might be able to fight them on this if it's something like "Nursery Water" that is specific for baby bottles--otherwise they will make you throw it out and you'll have to ask the cabin crew on the flight to get you warm water--the cabin crew will probably not bring you a full bottle of water to use at your leisure (we asked and they said no--on Delta, United, Northwest and Korean Air) so you'll have to keep pestering them every time you need water.
I packed powdered formula and then asked for hot water and mixed it with cool water to make warm water for the bottle. I have one of those formula portioning containers--where you pre-scoop the amount of formula into the container beforehand and then they are stackable and then it has an attached funnel with a lid for pouring it into the bottle.
With most formulas you're not supposed to mix them up and then wait hours to serve them--even if they are put in a refrigerator (it says this very directly on the labeling).
Also, be cautious about letting the cabin crew "heat them up"--because they probably will stick them in a microwave which not only can destroy the nutrition of the food--but if your bottles are not BPA free--can seriously leach chemicals into the milk. And when heating milk in a microwave it's very easy to get it scalding hot very quick meaning you might have to wait quite a while or ask for an ice cube to cool the milk down again. It's better to use warm water to mix the bottles on the spot. A
nd if you're bringing breastmilk, at security they will have you open up the cooler that you are storing it in and inspect it--they will not open up the individual bottles. It's better to heat breastmilk by sitting the milk in a hot cup of water and waiting for the hot water to heat the milk up--not a good idea to microwave it--the cabin crew will not go through the hassle to heat the milk by convection (with the hot water cup) so they will just pop it in the microwave--you can pretty much be assured of this--we had that experience when we flew from the States to HK with our son when he was 5 weeks old.
I would say: Just buy pre-mixed formula that is sealed.
