The energy is not exactly stored in the fossil fuels directly. Indeed you have to put in extra energy to break those bonds - pulling atoms apart is work. The “stored” energy comes from the fact that long time ago various processes split various compounds into two components, A and B. And putting them back together makes them snap like magnets with enough force to release some extra heat. We call A “fuel” since that’s the part that’s somewhat difficult to come by. We often forget about B altogether as it’s literally all around us. Fossil fuels are fundamentally efficient for flight since the oxygen is something you don’t have to carry around with you (unless of course you’re going to space).