Hi dks_34
welcome to this Apple (user-to-user) Community!
Re: Using an AMEX gift card + Credit Card to purchase a new iPhone
Am no expert in this area, yet your post to the community about the exciting purchase deserves some response.
As we are all Apple users, like yourself, in the community, we can not speak for what Apple will do to assist any particular purchase. If you are purchasing in a store, you could phone and ask first, as requirements likely vary from country to country and store to store. Apple Store - Find a Store - Apple
For payments using Apple Pay via Wallet: Apple uses the credit or debit cards that you added for Apple Pay.
For online purchases from Apple
Apple's "Shopping help" website provides payment details: see link below.
Eg: says: "Read about the variety of payment options you can choose from when you purchase from apple.com, and learn how the tax on your order is calculated."
See: Payment, Financing, Refunds and VAT - Shopping Help - Apple
Please note: I didn't see anything about gift cards that are not Apple Gift Cards.
(Amex Gift Cards may or may not be able to be used (eg: possibly, as Visa or Mastercard?) for purchases ?
Apple Gift cards generally need to be redeemed, before making use of them as an Apple Account Balance.)
While making an online purchase, there is generally an opportunity for contact with a "Shopping specialist" who can help with that particular purchase and payment.
All the best :-)