we had the same job done to two of our chimnys (its a 270+ year old place) One of the fireplaces serves the gas furnace and was a huge walk -in style cooking fireplace, the other was a chimney that served fireplaces on 2 floors. e paid about 9000$ (it was over 10 yers ago) and the SS lining (18 gage, I think) and the light spun fibreglas mortar was the big cost. They also hadda do some "sculpting" to fit liner with 2 smoke inlets in the big fireplace and had to install a new smoke-shelf and damper s ( I couldnt believe that We lived in this old stone uninsulated house for almost20 years without a damper and had water damage inside so many courses of fire brick hadda be added) and the chimneys also was rebuilt with new "old looking" brick. we also had 2 caps installed and that made huuuuge differences to the draft. Before, when wed burn logs in one of the bedroom fireplaces up stairs (We try to impress guests when they stay over in winter), the smoke sometimes returned down the chimney until the fireplace really heated up. That bedroom always had a slight wood fire smell.
The caps and screens were connected to the lightning rod systems (We also live on top of a big hill with only fields and pastures around.
Id say you were getting a decent price because inflation on material alone was pretty steep in the last 15 years or so.
My only aviv=ce is to check the gage number for th SS liner. The smaller the number the thicker the SS.