The oil furnace has been venting into this brick chimney for 50 years. It appears to be double-whythe brick, with a bit of mortar fallen out. Now there is an added gas water heater vent. I called for an inspection by a heating technician, along with a checkup of the old furnace. What scares me is the water heater was installed by a plumbing and heating company, and they obviously thought this was acceptable?
I’d say no, they’re plumbers not roofers, and I suspect they never went up on the roof to check the chimney. That other flue is an upstairs gas fireplace, appears to have a metal liner, or we’d hope so.