I've got this issue with my bike: the chain rattles an unusual lot when the bike is subjected to usual shocks during a very usual ride (or when I replicate that myself).
I've got a 21 speed bike with a Shimano tourney derailleur-shifter set and a KMC chain that's the same as what came with the bike (I also recently installed a KMC missing link, but the issue with the rattling predates that development). The chain rattles and touches other front chainrings when I ride on 2*x combinations (and is very annoying too).
Does the problem has something to do with the derailleur tension? I observed that when I pulled the derailleur back, the chain was more tense, so this could be a thing. If this is the case, then I would be tweaking the B-tension screw.
Or can it be something with the chain length? (Remember: the chains the same that came with the bike and when I measured the gap between 12 links, it came out to be less than 12 inches !)
I would really like this issue sorted to make my bike a nicer experience (I've taken up biking after a lag of an year or so and I really intend to keep it up and improve my performance) :)