Gidday,
Without actually hearing the bike to diagnose I would suggest that what you are hearing is just a ZX6 or 636 doing what it does...
They always have been (yes - even from new) & always will be a mechanically noisey engine & provided that it is not excessive will be fine - they do suffer from the "Kawasaki Curse" which is lazy camchain tensioneritis... If you are worried about it I would take it to your local Kawasaki Dealer & have them have a listen - trailer the bike down & let them run it up from cold...
I have yet to hear two of these things that sound the same mechanically so an educated ear is a definate requirement...
Don't second guess it get it looked at as that way you can be sure all is well...
Cheers

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