I'm a former Flight Attendant and I fly a lot with my children.
Airport security usually allows liquids through the airport in "reasonable" amounts, if they are intended for the baby.
I assume that your baby take powdered formula. This is much easier than ready-made and outside the U.S., in some countries like the U.K. they make you open ready-made, which means it could go off during your journey. Don't take any ready-made both for convenience and for getting through security.
Since there is no health advantage to a warmed bottle, instead of bringing boiled water, bring baby-suitable bottled water (like Evian or Vittel, it will be marked on the label) at room temperature. This way, you'll be able to feed your baby quickly and easily at any point of your journey. You then wont have to pfaff with any thermos, etc. For such a long journey, it will be MUCH easier to travel with just water bottles.
Also, I highly recommend the bottles with disposable liners. Avent, Playtex and some others use these. Traditional bottles are difficult to clean on airplanes. The sinks in the lavs are very low and a long stiff bottle wont fit. If you use these types of bottles, you will only have to wash the nipple and ring.
I pre-measured the powder at home before leaving and rolled the liners up. I put them in a zip-lock bag to keep them clean and then simply threw them away as I went. All I had to do while travelling was add water and shake. I could take A LOT like this so I was covered if there had been a delay.
Make sure though that you have enough bottled water. Do NOT depend on getting enough on board. We always ran out of bottled water on the airplane after the first service and there wasn't enough for formula-fed babies. Bring one or two from home and then give yourself enough time to buy water in the terminal, once you're past security. The water on the airplane is filtered tap and I've never heard of anything happening because of it so talk to your doctor if he or she thinks it can be given to your baby.
For more information, nine years ago I wrote an article on this subject. It's based on both my personal and professional experience of flying with children. It's totally non-commercial and other parents from around the world have contributed;
http://flyingwithchildren1.blogspot.com
Have a good time in America!