Thank you MukatA. That was very helpful.I will use 1040 NR form. What should I write for the line 22? Total income exempt by treaty from page 5, schedule OI, item L12?
Will J2 with EAD can also get the benefit of the treaty? Will they also need to use the same form 1040NR?
Thank you

The treaty benefit is normally reserved ONLY for the primary visaholder, I.e. the J-1 visaholder.

As a J-2 visaholder, you ARE a non-resident alien and will file Form 1040NR, but you get no treaty exemptions. Further, your employer IS required to withhold FICA (Social Security and Medicare) taxes.