Just a quick note about flying with liquid, including water for formula on a US bound flight - they will NOT let you take on your own bottled water in a thermos or otherwise. They will allow dry milk/ formula powder and pre-mixed liquid formula, but not bottles of water to mix with the milk powder. They will, however, provide you with bottled water on the flight (but it generally will not be warmed).
If you are going anywhere other than the US, they are much more willing to let you bring on your own bottled water (although I have encountered occasions - a flight to Japan and a flight to Malaysia) where they had additional gate screening and did not permit passengers to bring their own water. In both cases they supplied us with bottled water to mix with formula on the flight, no problem.