The student of geology and ultimately the public are asked to accept this statement entirely without proof, as indeed for the very long times proposed there can be no proof. There can be proof, and there is. For example, when a rockbed is stretched, any foreign things stuck in the rock will either elongate or shatter. Folded rockbeds often contain elongated sand grains, elongated pebbles, or even elongated fossils. And if you want to see the flow of a solid in your own lifetime, simply visit a glacier.
Fast glaciers can flow several feet in an hour.
For details see, for example, Structural Geology by George H. Davis. Geologists can and do account for this. Taylor has forgotten that the rockbed in question is buried. If the pressure from the overlying rock exceeds the tension, then all parts of the rockbed are under a net compression. Some parts are under more compression than others, of course, so given time and heat, the rock can slowly flow into a new shape.