Hi,
I am an A/V contractor and pull a LOT of wire.
If the wire , of which you speak, is double insulated and has a CL3 rating as long as it isn't touch the flue
you will be fine. 6" to 1' is plenty of distance.
Hope my answer is helpful. Although, I have a feeling you have already installed it.
But, maybe now you will have no worries.
Billy