So I was thinking of making a adapter plate for my lathe in the future. Would a old flange from a axle or wheel hub assembly be good material ?
My experience is that they're not good material. I havn't cut up every axle in the world, but I've cut up my share. They were once a good mid to high carbon steel, but they're selectively hardened, and (I presume) work hardened around the stud holes. They'll cut beautifully in "some" areas, and other areas just eat tools for breakfast.
As for the application, they're very thin, and not as true as you'd think they might be. You'll be cutting ALL of it. You're not going to "save" any factory surfaces.
After that, I'd still be nervous, as benmychree said, about galling, especialy on a threaded. If it's threaded, careful and dilligent oiling would be required every time, and it'd have to be refreshed fairly often. When galling happens (which it won't most times, but is in the very real realm of possibility), it's not only gonna be a "stuck" chuck, but there will be damage to the lathe spindle, and it's not the kind of damage you can avoid by advanced removal techniques. Galling is literally cold welded metal. No amount of heat or oil is other stuck thread extraction kung fu going to fix that.
If you had a different project in mind, an actual axle shaft (rear drive, solid axle) can offer up a very nice chunk of high (or highish) carbon steel in the shaft area inboard of the bearing race (or outer spline in a full floater), and outboard of the inner splnes. That area tends to be pretty workable. The spline and flange end though.... Very difficult to work with.