Snapper, not that far or with that many allergies, but we've been to and from the US many times with a little boy who is allergic to peanuts and dairy.
Here are my tips:
--if at all possible, fly with an airline that doesn't serve nuts as snacks. We only fly BA because they don't serve peanuts at all. It's ok if they can't guarantee the entire plane will be nut-free; they don't have control about what the other passengers will bring.
--tell them your dietary requirements and get the allergen-free meals for both of you, so that you can give him everything he'll eat and hoard the rest
--take your own food (maybe bagels? whatever you child likes to eat that's packable)
--eat right before you get on the plane
--take ALL of your EpiPens (get another prescription if you haven't got more than 3)
--also take: Piriton, an inhaler (even if he doesn't have asthma, an inhaler will help some reactions, especially if something bad gets airborne) and a steroid (prednisone or whatever they give him at the hospital here after a reaction). If he has a reaction, give him the EpiPen, the Piriton and the steriod.. if you have any questions about that and your GP seems unsure, just call the casualty unit and ask what they do. (The steroid will take a while to work, but you'll be in the air for a while, even if something bad happens.)
That's about it. The one thing we don't do is dope him up with an antihistamine before the plane. The good thing about a histamine reaction is that it's so visible, you can treat it fairly easily (at worst, with epinephrine until the antihistamine takes effect) and you'll see it even if there's just skin contact, so you'll know there's something there to avoid and remove.
I always plan for the worst and expect the best. It'll be fine, but it's reassuring to me, at least, to be prepared in case of emergency.
Good luck. Don't panic, you'll be fine. Now keeping him entertained for that long is another story....