(Interesting name ...) But it could simply be expansion and contraction of the metal. When it contracts, usually a 'side' or part of a side of the metal ducting 'pops'.
The only way that I know of to 'reduce' or eliminate the popping is to get the pipe to be a constant temperature. Also, round ducting doesn't have 'sides' like square or rectangular ducting so it doesn't pop. I wonder if your ducting in the fireplace is double-walled. And is it round? I don't believe you can 'insulate' the ductwork due to fire code issues. I suspect you'll have to get rounded ducting (if you don't have it), and double-walled ducting to boot.
I'm sure others will respond to your post. I'll be listening. My best to ya and hope this helps.