When a chimney doesn’t draft you get heavier build up quicker, smoking issues, glazed creosote build up and inefficient combustion just to name few issues. This chimney, lined with a stainless steel flue liners, vented a hearth stove that was installed on the original inner and outer hearth. As seen below the bottom portion of the flue, just above the the opening for stove connector, is extremely dirty and partially blocked by the build up.
The connector from the stove to the chimney flue was filled with build up as well. No wonder smoke was backing up in to the house!
The smaller the flue passage way gets the more draft and flow are going to suffer and the more problems you are going to have. After the initial sweeping the system is ready to be treated with a creosote modifier to help remove the rest of the baked on glaze. Re-sweep in a week.