The earlier Kawasaki ER6 had a habit of the exhaust cracking right where it joins the front down-pipe to the second part. It cracks all the way round, even if not too badly corroded, and can be hard to spot at first...
Check especially carefully at the joint. They can also be quite noisy from the fuel cap when venting air. If you pop the cap open and it stops, that's the cause. Other than that, if it is coming from the muffler area then it could be the internal baffling is starting to come loose in the silencer.
I have been riding my Kawasaki ER-6n for two years now and it's just started to make a whistling sound when it's idling and in motion. It is driving me insane. I have it to the Kawasaki dealer and they cannot find a problem.