Birds don't have mammary glands. That's what makes Mammals mammals.
Birds have the crop:
In a bird's digestive system, the crop is an expanded, muscular pouch near the gullet or throat. It is a part of the digestive tract, essentially an enlarged part of the oesophagus. As with most other organisms that have a crop, the crop is used to temporarily store food. Not all birds have a crop. In adult doves and pigeons, the crop can produce crop milk to feed newly hatched birds.[5]
Scavenging birds, such as vultures, will gorge themselves when prey is abundant, causing their crop to bulge. They subsequently sit, sleepy or half torpid, to digest their food.
Most raptors, including hawks, eagles and vultures (as stated above), have a crop; however, owls do not. Similarly, all true quail (Old World quail and New World quail) have a crop, but the Buttonquail or Turnicidae do not.