First thing is safety. Make sure your roof setup is safe to work off of and always wear gloves dealing when installing flexible chimney liner. It is very sharp. Before you install the flexible chimney liner, you need to check inside the chimney for any possible obstructions and remove them first.
Then install the tee on the chimney liner. Insert the chimney liner from the top down. Some installations may require you to use a rope connected to a pulling cone. A second person may be needed to pull the rope from the bottom of the chimney while the person on the roof guides the liner down the chimney.
Avoid trying to push the liner down and force it, always try to twist and turn the liner and pull from the bottom. Have a person on the bottom waiting with the snout of the tee. You need to communicate with each other and line up the hole on the tee with the snout. The most important part here is that the lips of the tee body are 100% inside the snout. Once they are in tighten the band and you are done on the bottom.
The top can now be finished. Install the top plate with a bead of silicone on the bottom. Pull up on the liner to remove any slack and tighten the band on the top plate. After the top plate is installed you can cut the extra chimney liner. You can use a hack saw or a an angle grinder to cut off the excess.
Now install the rain cap. The rain cap slides over the collar on the top plate and secures with a band clamp.
Now that the liner is all set and will not move anymore, you can fill in the gap between the snout on the liner and the masonry wall. You can use small pieces of brick or special insulation designed for this application. Then cover it with mortar or refractory cement.
That is it, you are done. If you have any trouble installing the liner you purchased from www.ChimneyLinerDepot.com, call them and they will help you through it.