I don't think the responders read his post closely enough - he's putting together the FAK for his (Boy Scout) Troop. I've never heard of any Troop with an airway kit, despite possible training by one or two adults or patrol leaders to maybe use one. Troop kits tend to have medical supplies for Scouts and adult leaders with general first aid training. Would you want the airway to stay in the FAK after you move on from Scouts in a few years?

The answer is no, don't include an oral airway in your troop FAK.