Lining chimneys is a common place practice these days, especially with the rise in people fitting new stoves and burning wood.
There are a couple of points though that might go un-noticed when specifying / getting quotes for a flexible liner.
Firstly there are two grades of liner. One (and this will probably be the one that you are quoted for) comes with a 10-15 year guarantee and is called a 316 Grade. The other is a thicker grade and comes with a 20-25 year guarantee, this is known as a 904 Grade. Price difference between the two is around £10 per metre and given a normal house height of 9m, this will equate to around £100 difference. Given that this will be a fraction of a fitted price I personally specified a 904 when we had our chimneys done.
Secondly there is the insulation. Most fitters will not insulate the chimney, but it is recommended that this is filled to help stop condensation issues with the liner. It should also help stop any old soot from being burned off from contact with the new hot flue. So it is worth enquiring about insulation options when lining an old chimney.