Two-dimensional (2D) semiconducting transition metal dichalcogenides (TMDs) are good candidates for high-performance flexible electronics. However, most demonstrations of such flexible field-effect transistors (FETs) to date have been on the micron scale, not benefitting from the short-channel advantages of 2D-TMDs. Here, we demonstrate flexible monolayer MoS2 FETs with the shortest channels reported to date (down to 50 nm) and remarkably high on-current (up to 470 uA/um at 1 V drain-to-source voltage) which is comparable to flexible graphene or crystalline silicon FETs. This is achieved using a new transfer method wherein contacts are initially patterned on the rigid TMD growth substrate with nanoscale lithography, then coated with a polyimide (PI) film which becomes the flexible substrate after release, with the contacts and TMD. We also apply this transfer process to other TMDs, reporting the first flexible FETs with MoSe2 and record on-current for flexible WSe2 FETs. These achievements push 2D semiconductors closer to a technology for low-power and high-performance flexible electronics.