Air flows upward in the wick of a lantern because of the liquid property called

Adhesive.

Adhesive is the force of attraction between molecules of different kind. Liquid flows upward the wick because the adhesive force between the wick and the liquid is higher than cohesive forces in the liquid.

When the adhesive force between the wick and the liquid is high we have capillarity taking place. This cause the liquid to move up the wick.