I suspect the noise you're hearing is the stretched chain riding high on the new clutch sprocket.
Your large bottom sprocket is worn badly. Throw out the #35 roller chain and lower sprocket before you ruin the clutch sprocket again. Think about investing in some sticky chain lube.
I would almost bet the whistling you're hearing is wind shear between the outer and inner sprocket because of the threaded holes on the inside when the motor is idling and the clutch has not enguaged.
Old clutch
Bad
is it possible that the new clutch is rubbing somewhere?
I just put a new 12 tooth clutch on my go kart (this one: http://www.ebay.com/itm/231026314330?ssPageName=STRK:MEWNX:IT&_trksid=p3984.m1439.l2649 )
Now, with the new clutch, a whistling sound came from it! Could that be because its too loose? or just because its new? I oiled the main bearing (not inside it!)