So MIXR (previously called OpenEaagles) is a framework that would be used to build something like FlightGear (as I understand FlightGear to be). In MIXR, there are a few "dynamic models" for flight, one of which is JSBSim. Others include the so-called RAC model (very simple) and Lareo (better than RAC). The term "better" concerns itself with what you want to do (i.e., simulate). If having a bunch of entities / aircraft moving around is the desire, RAC and/or Laero might work just fine. If you want to interact with the model (such as a pilot), then a more detailed model (such as JSBSim) might meet your needs.
I assume, that within the FlightGear source code, there is a flight dynamics model (maybe even a few) that have been implemented. To use those with MIXR, the source code would be extracted and probably packaged so that is interfaced to the framework much like JSBSim is.
For graphics, MIXR provides a decent framework to construct that. In the end, a FlightGear kind of application could probably be built using MIXR as a starting point for how things are generally organized and assembled.
I will admit, I've not really ever used FlightGear in a meaningful way. Others (in the past) have commented that it would be interesting rebuilding FlightGear as a MIXR app.
Hope this helps!
Doug