For four months, the B-1B bombers of the U.S. Air Force’s 9th Expeditionary Bomb Squadron relentlessly hit Islamic State fighters in eastern Kobani from the air, slowly watching the line of control in that city swing back to Washington’s Kurdish allies.

The air tactics developed over Kobani, senior U.S. officials said, will hopefully prove to be a model of what close communication between an allied force on the ground and American aircraft in the skies can do. The lesson of Kobani, officials said, will be tried again when...