There's a very knowledgeable & experienced chicken breeder/keeper in our poultry club. I told him about the hen who choked to death at check-in at this year's Fair. He told me how he helps chickens that are choking like that, he first tries to remove as much food as possible from the beak, by tapping the beak on something firm and/or prying it out with a finger, then he puts his mouth on the beak & blows the remainder down the bird's throat.
Do this at your own discretion. I haven't tried this, but trust this man's advice & will follow it if ever I'm faced with a similar situation.