Both Jenkins and Flynn say they need to "rethread the Loom." A loom has two types of thread on it: warp (the up and down bits on most looms, including this one) and weft (the side-to-side bits on most looms, that are manipulated with a shuttle to create the cloth). The correct term is "re-warp a loom."
Several characters (including Flynn, who should know better) refer to the Loom of Fate being cut. A loom is a structure that holds threads being used to weave cloth: it's the big wooden thing. The Loom of Fate was not itself cut; the cloth on the Loom was cut.