I agree with the guys that say this setup needs separate flues.
The temperatures of wood burning stoves is much much higher up 500+ degrees F .
Creosote residue in a flue with a much “colder natural gas burning appliance” Is NOT recommend.
The colder burning natural gas will release a lot more moisture in the flue, maybe sweating inside the flue since the chimney sizing issues are probably wrong.
Natural gas burning appliances need (generally smaller flues) for proper operation then wood burning fire places. So end result is a flue that is too large for natural gas products of combustion to be “drawn” up the chimney.
Acid from the water combining with the creosote could be the next issue. That liner better be a good stainless steel but again we come back to the issue of two separate fuel types…
I highly recommend a complete evaluation by a CSIA tech or a similar tech.
Also check out Gamanet.org
For topics on natural gas and proper flue function. Great info for all .