The least efficient plane[0] burns 1 gallon per passenger every 64 miles. A 3,000 mile flight will burn 47 gallons of fuel per passenger.
A stick of gum can be up to 7 grams[1]. Let's assume it's even heavier once chewed, and is a nice, round 10 grams.
If we assume the mean passenger weighs only 50kg (or, 5,000 pieces of gum), then each piece of gum is responsible for 9.4 milligallons of fuel for that trip. Or 1.2 fl-oz.
Now if we consider that there is gum all over the plane, maybe a soda-can's worth of jet fuel is burned up ferrying it all around. But that's with optimistic passenger weights, pessimistic gum masses, a gas-guzzler of a jet, and probably a calculation error I've made converting between all the different units above.
:)
[0] https://en.wikipedia.org/wiki/Fuel_economy_in_aircraft#Airli...:
> On the other side, the least efficient was British Airways at 27 pax-km/L (3.7 L/100 km [64 mpg‑US] per passenger), using fuel-inefficient Boeing 747-400s with a low density of 0.75 seat/m2 due to a high 25% premium seating, in spite of a high 82% load factor.
[1] https://en.wikipedia.org/wiki/Chewing_gum#Product_varieties
> Chewing gum can come in a variety of formats ranging from 1.4 to 6.9 grams per piece, and products can be differentiated by the consumers' intent to form bubbles or the sugar/sugarless dichotomy.