Be careful to consider the implications of 2 flues side by side. One flue may draw smoke into the home from the other under if the house is in a negative pressure event.
Talk to your architect/ mechanical contractor/ mason /contractor about the condition. When the heat comes on the return air side can back draft one into the other. For that matter. Same can be said for the cooking exhuast hood. If the hood is over 400 cfm, make up air is probably required, you do not want the makeup air coming from the fireplace.

Enjoy your time in God's country.

I don't know if this would be an issue since one is outside. They should never pull off of one another.