I can re-line your chimney for you and connect it to an existing appliance, but this is basically a new install.
There are some things to consider before going ahead.
When the old system is removed, what will we find? How much work will need to be done to make it ready for the new system?
What sort of fuel are you going to burn: Wood only or multi-fuel (peat, smokeless fuel, etc)?
Do you ever 'slumber' your fire: keeping it 'in' for long periods of time, i.e. overnight?
There are many brands of liner on the market today; and they are not all equal! However, there are only two sorts of flexible steel liner on the market, manufactured for different purposes.
There are gas only (Class 2) and Solid Fuel liners (Class 1), there are generally two sorts of alloy used depending on whether you want to burn wood only or multi-fuel use. The main difference is in the ingredients used to make the stainless steel alloy (316 or 904).
I will always look to use the best quality materials available, cheap as chips equipment doesn't stand the test of time, it's false economy in my opinion. I would always recommend the highest quality liner you can get as not only do these have better corrosion resistance, but also a much longer warranty period.
The difference between the grades of stainless steel used in flexible chimney liners is primarily corrossion resistance. 316 is less resistant to sulphuric acid than 904 steel; given that flexible chimney liners are composed of two thin layers of steel - one corrugated on the outside and one flat spiral on the inside - with a combined thickness of 0.5mm or less!
A chimney operates on the principle of having a natural up draught. One factor in creating the up draught is maintaining a warm flue gas temperature, of between 150°C and 450°C. Burning wood or multi fuel slowly with insufficient air supply, particularly on stoves or closed appliances must be avoided. Low flue gas temperatures will cause condensation and greatly increases the risk of producing excessive tar and corrosive soot deposits. This is a common problem, particularly when burning wet wood or coal and should be avoided. If soot and condensate deposits are allowed to accumulate in a flue, the deposits can ignite causing a chimney fire. These deposits can also be very corrosive and if they are not regularly removed can cause corrosion of the metal parts of both the chimney and the appliance.
Warmth - If a chimney stays warm throughout it's length then it stays dry, if the flue gasses drop below 100ºC then condensation will occur and with it residues. If the flue is lined with soot, then this condensation will cause an acidic environment. The best way to keep a flue warm is to insulate it and...
Watertightness - If rain runs down the inside of a nice warm flue, then it will quickly evaporate; however, if the flue gasses cool below 100ºC then the rain will cool the flue further and run further and further down the flue, cooling it as it goes; again leading to the creation of an acidic environment! This also applies to the outside of the liner, which will probably be in a used chimney flue of some sort, even if the chimney has been thoroughly swept there will still be some rediue on the walls of the chimney. If condensation and water are allowed into this space it will adhere to the outside of the liner corroding it from the outside (beware of liners that do not have the same grade steel on the outside skin as the inner skin).
Other methods of re-lining a chimney
Cast In-situ - A 'sock is inflated in the chimney, several holes are opened to ensure the sock stays central in the flue and a ceramic/concrete is poured around the sock which is then deflated and removed. Requires building work to centralise the former (sock), great when done well; however, if not done to high standard this will leave gaps, thin areas and bare patches.
Furanflex - A resin 'sock' is lowered into the chimney, this is then inflated, then steam is blown into the sock which sets solid after about a few hours. The resin tube is then trimmed and the areas around the top and bottom finished appropriately. Can be used to re-line all sorts of liners and pipes. Has been used on antique rainwater downpipes, industrial units up to 2m diameter...different classes of resin for different environments.
Eldfast - An over-sized 'sponge' is drawn up the chimney as a ceramic/cement mix is poured down the chimney. The 'sponge' squeezes the mix around the chimeny lining coating the flue and filling cracks and gaps. Can leave 'bare' patches, especially on bends.