llesson,
If enter the U.S. on a J-1 Visa, you will be able to train and work.
The J-1 Visa will allow you to stay in the U.S. for a total of two years. When you complete all our FAA rating up to and including Flight Instructor, you will be able to Instruct for the remainder of your Visa. i.e. It takes you 6 months to get to Flight Instructor, you can instruct for 18 months. Total stay in the U.S. cannot exceed two years.
(I know I repeated myself several times in the prior paragraph, but people get confused over the rules for the J-1 Visa, so I try to state it as many ways as possible to make sure people understand it clearly.)
Two References for you:
1.
TIPS FOR U.S. VISAS: Exchange Visitors
2.
U.S. Consulate General Perth
Good Luck,
Capt. Richard J. Gentil, Pres.
Naples Air Center, Inc.