Which current commercial flights have the highest ETOPS ranking?
Air New Zealand's Auckland (AKL) to Buenos Aires (EZE) is the longest ETOPS flight I know of, under ETOPS 330. It started in 2015:


  Air New Zealand completed the first flight approved for 330-minute extended twin-engine operations (ETOPS), flying a 777-200ER powered by Rolls-Royce Trent 800 engines. The December 1 flight departed from Auckland, New Zealand, and landed in the Argentinian capital Buenos Aires about 12 hours later.


As for ETOPS 370, I'm not aware of eny regular commercial flights, but some candidates are Sydney-Johannesburg and Sydney-Santiago de Chile