No, technically penguins cannot fly

Penguins are birds, so they do have wings. However, the wing structures of penguins are evolved for swimming, rather than flying in the traditional sense. Penguins do “fly” underwater at speeds of up to 15 to 25 miles per hour.

As adept swimmers, penguins spend a lot of time in the water. Some penguins spend up to 75 percent of their lives in the water. Like other birds, penguins do lay eggs and they raise their chicks on land.

All penguins live in the Southern Hemisphere.

For more information:

Penguin Adaptation, NASA QUEST

Seabird Research Program, Southwest Fisheries Science Center

Arctic & Antarctic Activity Book (pdf)