Is there an estimate for the length of the American Cordillera?
A difficulty in finding a resource that provides an estimate of the length of the entire American Cordillera is as, @fre0n states in the comments


  there is very few standard mention regarding this unit as a whole, instead it is more often localized


As can be read in the Wikipedia article American Cordillera, where they state that


  The American Cordillera is a chain of mountain ranges (cordillera) that consists of an almost continuous sequence of mountain ranges that form the western "backbone" of North America, Central America, South America and Antarctica. It is also the backbone of the volcanic arc that forms the eastern half of the Pacific Ring of Fire.


The Wikipedia article lists the constituent mountain ranges as being a line of overlapping mountain ranges from the Alaska and Brooks Range right through the Andes to the southern tip of South America, also suggesting that the Cordillera could


  possibly be followed through the arcuate South Georgia Ridge across the Southern Ocean to the mountains of Graham Land on the Antarctic Peninsula.


Given the earlier definition of the Cordillera being


  an almost continuous sequence of mountain ranges that form the western "backbone" of North America, Central America, South America and Antarctica.


according to Google Maps, where I used this definition and traced the distance (right-click on map -> Measure distance -> select points along the 'spine' of the Americas and Antarctica), I determined an estimate of the total length as being approximately 17,000 km (or about 21,500 km if the South Georgia Ridge and Graham Land Mountains are included).