Seems like it is policy to be able to use more than 3 over the phone.
How many Delta Gift Cards can I redeem at one time? Up to 3 gift cards can be redeemed per transaction on delta.com. If you wish to redeem more than 3 cards for a single purchase, please call 1-800-221-1212 and a Reservations Specialist will be able to assist you.
https://www.delta.com/content/www/en...card-faqs.html