Virgin Atlantic doesn’t fly JFK-AUS. That’s a code share. Even if they did operate it, it wouldn’t be 5th freedom.

Fifth freedom is airline from country A operating flight from country B to country C. But JFK and AUS are in the same country, so that’s why such a route wouldn’t be 5th freedom.

Only route within the US like that would be Qantas LAX-JFK. And no you can’t fly it stand-alone.

An example of 5th freedom would be Cathay Pacific flying JFK-YVR, which you can buy stand alone.