Jet Propelled Animals
There are some animals which use jet propulsion already. No, they mostly don't fly in the air, and no, they don't really use combustion to produce a stream of matter with which to jet. These creatures also tend to not use continuous propulsion, which is much unlike our current jet engines. They do, however, condense and force liquid out of a nozzle, which they then direct to move. I'm talking about Japanese flying squids and those mysterious Salps!
It should be noted that jet propulsion does not mean that the propellant is some flammable material. If you're looking specifically for an animal which uses combustion in their jets, I'm afraid I don't know of any such creature. I also doubt its existence.
The best creatures to modify for jet propulsion are those which have close relatives who already use it! It would be just a matter of figuring out which evolutionary pressures made the organisms develop jet propulsion, introduce those pressures, and let the process of evolution go! Alternatively, you can just mess with their genetics until you get what you need.
Modifications for Flight
Squid would need to be capable of breathing air (without drying out) and using that air to propel themselves. The Salps need a more rigid body in addition to the adaptations that squid need. These creatures may need additional modifications depending on how fast, how far, and how quickly you need them to travel.
If you are still looking for a jet of combusted matter, they would need some major tweaking. Their bodies would need to have a safe combustion chamber. They would need to produce enough combustable material to propel themselves. They would need to regulate how much fuel they have in themselves. Their jet-nozzles would need to become more heat resistant. Their bodies would have to cool their combustion chambers so they don't cook themselves, or be modified so that their combustion chambers are cooled by some other means.
Depending on how high they go, they may need more modifications, such as those found in avian lungs. Avian lungs allow them to maintain their blood oxygen level so they can fly higher. They're also nifty because of their unidirectional air flow!