The car does not have a normal radiator cap.It has what is called a Degas bottle which also holds the reservoir.l was going to back flush the heater core,but a lot of people advised against doing that.So how do l properly flush the cooling system on this vehicle.Should l keep the engine running while flushing?Please help.

an easy way to do it is this. (do all of this while engine is cold)
Drive it on to ramps or the curb so u can get underneath to open the petcock on the bottom of the radiator. Now loosen the petcock, but dont let fluid leak out. (get it almost open so u can easily get it loose when the car is warm) Now take off the radiator cap & let the car idle & warm up. Get a garden hose ready. once warm gently open the petcock & let it drain.. go ahead & turn on the heater to full blast.
Now start to feed the reservoir the water from the hose. u can turn the hose down to match the flow of the petcock & the system will not get any air bubbles in the heater core & will flush properly. Once the water comes out clear, shut off the car, let it all drain out & close the petcock, & refill the radiator with a 50/50 coolant mix

there is a fair amount of coolant in the engine block just flushing the radiator is not enough. Have u checked with a dealer of garage on having it flushed its well worth it newer cars need a bit more attention to details then older ones did to ge tit properly flushed & refilled l find it worth ever penny to take it & have the professionals do it. But if u insist on doing it yourself do not use 50/50 mix because u wo not have all the old coolant out so 50/50 may not give u the protection u need since u r mixing it with what is left in the system.

If you really want about your Lincon Town Car, you should check out the Lincon owners forum
http://lincolnforums.com/lincoln-town-car.html

My brother who has a Lincon has asked lots of questions and got really good from lots of other Lincon owners.