Phone Number Of Delta Airlines Skymiles 1-800-323-2323. Information concerning the contact numbers of Delta Airlines Skymiles customer service and how to contact them are mentioned below. Get help and support for all the services that Delta provides such as immediate reservation assistance, lost baggage claims, information with cargo department and medallion status. For general travel help and tips, you can tweet to Delta customer service by using @Delta, who are available 24x7