Delta Airlines Provides Priority Phone Number For Flight Bookings And Cancellations Delta Airlines has upgraded their phone booking system so that if a customer calls to book a flight, they can make the reservation over the phone. An important part of this process is having a priority line for those who need to cancel their plans or reschedule for an earlier flight. This ensures Delta customers have the option to cancel or rebook without experiencing any hassle. Delta Airlines has upgraded their phone booking system so that if a customer calls to book a flight, they can make the reservation over the phone.