A group of swallows is most commonly called a flight of swallows.

You’ll also sometimes see several other collective nouns used for swallows, including:

  • a swoop of swallows
  • a gulp of swallows
  • a richness of swallows
  • a kettle of swallows
  • a herd of swallows (rare/whimsical)

In everyday English, flight is the most widely recognized and “safest” term to use for a group of swallows, while the others appear more in nature writing, trivia lists, and bird-enthusiast discussions.