As of August 2015, Delta Airlines allows the purchase of SkyMiles through your SkyMiles account, but not Medallion Qualification Miles. Delta has only allowed the purchase of MQMs through end-of-year promotions in December 2013 and December 2014.
During the 2014 Medallion Qualification Miles promotion, MQMs were available for purchase in increments of 2,500 miles and up to a maximum of 10,000 miles. Costs per mile depended on Medallion status, and general SkyMiles members paid $625 for 2,500 miles, Silver members paid $725, Gold members paid $925, and Platinum and Diamond members paid $1,025. Earn MQMs year-round by flying Delta Airlines or by using a Delta Airlines Platinum or Reserve credit card.
To purchase SkyMiles, log into your SkyMiles account at Delta.com, and click My SkyMiles. Click Buy, Gift, or Transfer SkyMiles on the sidebar, and click on Buy Miles. Select the number of miles you wish to purchase, and click Add to Cart. Miles are available in increments of 2,000 miles, and you may purchase up to 60,000 miles each year. Click Check Out Now and then Pay Now. Enter your credit card and contact information, and click Confirm Purchase to purchase your miles. Miles appear on your SkyMiles account within 24 hours.