Hi Celtic,
Depends on what stage you are teaching. If you are required to give any endorsements, i.e. PPL training you definitely need FAA ratings. You can teach on your JAA licence if you are training for JAA CPL or IR training you do not need FAA FI ratings. However, it will be difficult to work with out a proper work permit and given the conditions after September 11 I am sure it wont be easy to get a work permit.
Cheers,
Jatin