Is it possible to reuse the languagesettingswithflags web part from v8 in v9? I had thought about just copying the webpart code from v8.2 into my v9 code base.
You have two options:
a) You can use new Language data source webpart which substitutes old Language selection, Language selection drop-down and Language selection with flags webpart. This is prefered way so you can easier customize desired behavior. You can see proper configuration of this webpart eg. on sample Corporate site (v9 instance without upgrade).
b) If you want the same behavior as you`ve had in v8.2 you should read doc article Recovering abandoned features, web parts and widgets where you can find how to recover Language selection with flags on your v9 instance.