getI() can be used to retrieve the inclination of a satellite from its
In which frame is it returned? I understand it is returned the frame in which the state is defined.
Is it possible to get the inclination in another, specified, frame, eg.
FramesFactory.getTOD(IERSConventions.IERS_2010, false)? maybe using some transform method?
Yes you need to perform a frame conversion of the orbit.
But there are built-in function that can help like
incInMyFrame = new CartesianOrbit(myState.getPVCoordinates(myFrame), myFrame, myState.getMu()).getI();
Hope this helps,