Your genetic engineers are going to need to be very creative, and the horse is not going to be the basis of an organic jet engine.
In the natural world, jet propulsion does exist with squids, octopi and some other related creatures. Generally, they draw water into a sack and forcefully expel it though a siphon or similar tube. This might serve as a sort of JATO take off mechanism, but certainly not for continuing flight.
What will be needed is some sort of worm like predecessor. Air or water (for a water jet) is taken through the mouth/inlet, and would be compressed through a series of annular muscles in travelling waves through the "gut" until it has been compressed to sufficient degree, then released out the back end, which has been presumably engineered into a convergent/divergent nozzle to produce thrust.
This might work well on its own for a water jet powered boat, but compressing air enough to create usable thrust isn't going to be so easy. For a jet propelled aircraft, the creature will need some sort of mechanism to convert food into a fuel (some people's gut bacteria convert food into alcohol, so there is a precedent), and an ignition mechanism to create combustion in the "expansion chamber". An elaborate series of sphincters will have to be engineered in to meter the fuel, prevent the flame from moving up the tube to the "intake" and so on.
Essentially what you have here is a sort of organic pulse jet. Pulse jets were explored as aircraft propulsion units during WWII (especially by the Germans), but pulse jets tended to be much larger and less fuel efficient than even primitive 1940 era turbojets. On the other hand, they were much cheaper and did not require the scarce resources that turbojets did, so the were extensively used on V-1 missiles, and large numbers of cheap, semi expendable fighter designs were considered in the closing days of the war as well. The Luft 46 website (http://www.luft46.com) has lots of interesting conceptual designs to choose from.
How you work this into your jet propelled creature is up to you. Since this organic pulse jet is probably not going to have a lot of power, a single "pulse jet worm" will probably only be able to carry a small load a limited distance. You may consider something along the lines of a Remora, which can be attached in a parasitic relation to the actual flying creature. with multiple units attached for flight, and then detached and thrown in the feeding tank for "refuelling" after each use.