Check out Wrightslaw--
look for the Letter to Gloucester. (it may be in a link here, too-- you could try searching the term)
That alone should demonstrate that a life-threatening food allergy is a qualifying condition.
You'll also need some MEDICAL documentation which attests that your child's allergy is life-threatening in nature.
Remember-- eligibility FIRST. No, no, no, no accommodations talk BEFORE eligibility is determined/evaluated. Gently steer back to that if they try to get ahead of things into specific accommodations as a test of whether or not a 504 is "needed" or not.
Also-- DO NOT grant unfettered access to your child's physician or medical records. They don't need it.
One more--
Do NOT sign a waiver of anything-- particularly not a waiver which limits their obligation to administer life-saving medications. Period.