If you use you're 2 years in the United States on a J-1 you then become 'ineligible' for 2 years unless you can get them to give you a waiver.
There is no legal status for a CFI other than J-1 as the job does not meet the criteria for H-1B and the Green Card, if you can find a sponsor, has a long waiting time as a CFI would be regarded as a Third Preference occupation. I believe the wait is currently about 6 or 7 years. Your potential employer would also have to file with the Department of Labor to show they can't find an American to do the job. Basically, this is never realistically going to happen.