Back in the days KLM operated its own Rembrandt lounge at JFK, I don`t know, what happened to that grand old lounge.

Beside that KL don`t operate any Lounge in the US, as far as I know.They certainly use WC`s and some other lounges on individual contracts, like the BA lounge at MIA or the Air France/Sky Team lounge at YUL.
Before they cancelled the ATL nonstop ex Schiphol, you got an invitation to the Delta International Biz Elite Lounge at ATL.