Do you want the fireplace for heat, or for looks? Because fireplaces are heat LOSERS. Commonly called "negative" heat. The room heat goes right up the chimney.
We had a "zero clearance" or prefab fireplace in our last house. It wasn't efficient at all so we installed a woodstove insert in it. The fireplace flue was 8 inches and the stove flue was 6 inches.
Now if you want the fireplace for heat, then look into an airtight fireplace from the woodstove manufacturers. They look JUST like a fireplace but are heaters. And they have 6 inch flues.

The area of a chimney flue is determined by the area of the fireplace opening so you only need to get a small fireplace.

One brand of prefab wood burning fireplace with a 36" wide and 29" high firebox opening has a 10" inside and 15" outside metal chimney diameter.

I like the "negative heat" idea. From a wood stove brochure no doubt.

Any wood burning appliance that opens up so you can see the fire will have a larger flue than a heating stove or the room would fill with smoke.

there are two classifications decorative meaning just that most of the heat goes up the chimney
The other classification is high efficiency Essentially it is a wood stove fireplace listed with an Epa efficiency rating If you are looking for a positive heat gain then purchase an EPA rated fireplace If you don't care and want a negative heat loss t and only want aesthetics of a fireplace then purchase the decorative models not EPA rated. They tend to be much cheaper and made that way as well

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