Once I have created a flight, I save it by selecting the MORE option on bottom of the screen (or pressing the SPACE bar) where I created the flight, and there I see another list of choices including LOAD/SAVE (SPACE bar again), and then a box pops up that gives you the option to load/save the flight or flight plan. To save the flight plan, you need to change the save file type from .FLT to .PLN because by default it selects .FLT. I also get to save the flight/plan to the PC or the XBOX cloud storage (and the option to delete from the XBOX Cloud storage).

If you choose to save the flight plan rather than the flight itself, then the flight plan can be loaded for different aircraft. ;)