A spontaneously evolving creature would likely fail more than one or two of your requirements.
It would be quite a stretch but here is the closest I can fit what you'd describe. I'd use a bombardier beetle as a template. Based off that, we have a winged organism that can produce a strong chemical reaction internally with the ability to direct the result.
If we assume that hydrogen peroxide (H2O2) is the desired propellant, we solve a few issues. Decomposition products are hydrogen and oxygen. Reserves of each gas can assist respiration and a fuel source. Bombardier beetles use hydrogen peroxide, hydroquinones, enzymes and water to produce their jet. A short stretch would be a creature that can focus on hydrogen peroxide.
Direct oxygen production would allow high altitude flight and allow a larger creature. Dragonflies have been show to increase size up to 20% in hyperoxic environment. http://www.wired.com/2010/11/huge-dragonflies-oxygen/ Canada Geese can fly up to 1000km in a day and have been spotted up to 9km altitude. http://en.wikipedia.org/wiki/Canada_goose
Fuel ignition could be started with compression, like a fire piston. 671
Pistol shrimp can create enough force to cavitate water. It would be a small step to have a chitinous chamber to compress a gas mixture to autoignition temperature. Sustained firing would be extremely difficult due to the force and temperatures. Conceivably, the burst could be for takeoff or additional speed.
Size and energy conversion would be the limiting factor for this imaginary creature. Any creature with an exoskeleton has to molt to grow. The old chitin is shed and the new chitin has to harden. This would leave the creature completely defenseless while the process happens. Any interruption could lead to a deformation serious enough to cripple it until the next molting. Supporting it's own weight would be difficult, let alone passengers, barding and gear. Without gliding, flight would carry a huge energy load necessitating huge amounts of food before each flight.
With a stretch, a gigantic bug that can produce a hydrogen peroxide fuelled, organic jet burst could grow large enough to support passengers and be pushed to fly extreme altitudes and distances. 671