Looks like you'd need two things: a couple of tubes to simulate the upper respiratory system (mouth, nose, throat) and parts of the lower respiratory system (trachea, bronchi) and something inflatable to simulate the lungs.
I'd probably go something like red licorice sticks or tubular pasta to simulate the nose/mouth leading down the throat and continuing to the trachea. At the end of the trachea, you could split the tubes into the "Y" to make bronchi.
To make the "lungs" you should use something elastic and inflatable. Gum came to mind for me. However, it'd have to be pretty well-worked gum (prechewed...) to ensure its compliance. You'd have to make it into a sort of bubble, and then seal the rim of the bubble on the end of the red licorice/pasta.
However, there is also the option of making them not necessarily animated, in which case you could get anything pink and moldable, really for the lungs. You might even be able to buy some cheap ground beef, mold it, and seal it in a few layers of plastic wrap. Another fun side of this is that you could also push your kid to demonstrate the dangers of smoking on one lung by putting a ton of pepper on it (to show the carbon deposits that smoking leaves). I'm sure that'll be inspirational for the class.
Finally, depending on how loose the definition is for "food," you might just hit a butcher shop and pick up some animal lungs. You know, if you're in a hurry!
Hope that gives you some ideas!