No fission reaction, just radioactive decay in Dragonfly's case. It will use an RTG (radioisotope thermoelectric generator) not unlike Curiosity and most missions to the outer planets to date.

Just a note - radioactive decay is is fission, since it involves a nucleus splitting apart.

No, not quite. One of the types of radioactive decay is spontaneous fission, but it's not relevant in the context of RTGs. Alpha decay (the emission of a 4He nucleus) might in principle be called "fission" but in practice is not. Beta decay involves no splitting whatsoever.

RTGs are heavy; I suppose this means that it'll park itself for a long time to charge its batteries and then do a quick flight and repeat. Which sounds like it could work pretty well for this use case.

On the other hand, a hot-air balloon kept aloft by excess heat from radioactive metal might be a more attractive option if we were selecting proposals based on awesomeness.

Does that mean a nuclear powered cruise missile could stay airborne until mechanical failure? That would make future warfare... interesting.

It isn't all that much of a game changer. Mid-air refueling means that bombers can stay airborne a long time. Four or five bombers rotating back and forth can maintain one "on station" continuously. So the capability is already there. This tech would just make it more scifi.