2001 Lincoln ls
Do NOT flush the transmission. A flush will pick up that small debris, the junk, that lays in the bottom of the pan or in filter, and does no harm. Many cars have a magnet in the transmission pan, ( My Toyota has that) that collects steel dust. A flush disturbs all that and circulates it through your transmission doing far more harm than benefit. Then also, some places use solvents in a flush that never get entirely out. It does nothing with the torque converter either.
But to answer your question a coolant flush/replace coolant about $125. Transmission about the the same, so for both at least $250
Looking for a Used LS in your area?
CarGurus has 511 nationwide LS listings starting at $2,595.
Search Lincoln LS Questions
Lincoln LS Experts