If taxes on jet fuel are reduced substantially, the equilibrium quantity of charter flights will go up, but the price will go down. This is because supply will rise in this situation.
One of the non-price determinants of supply is the cost of inputs. Jet fuel is, of course, an input for charter flights (assuming they are flown by jet aircraft). When the cost of producing a given good or service goes down, the supply of that good or service goes up.
An increase in supply is shown on a graph by a movement of the supply curve to the right. When the supply curve moves to the right, a new equilibrium (the point where supply and demand curves intersect) is reached at a higher quantity and a lower price.