What are the limiting factors when trying to print flexible filaments with a Bowden extruder setup? Other than the most obvious issue with the filament kinking in the tube, what other issues could arise when trying to print flexibles (i.e. TPU/TPE, Nylon, etc.) with a Bowden style extruder setup? 

Can the kinking issue be alleviated by a well-constrained filament path (proper ID) in a properly sized Bowden tube?
As a user of an UM3E, which uses Bowden tubes and has TPU as an available material, I can tell you that the kinking issues can be alleviated or downright avoided. 

I've printed quite a few things with the Ultimaker-brand TPU 95, and never had problems with kinking in the tube. 

Ultimaker uses 2.85 mm filament, with Bowden tubes adapted for those and a rear motor, i.e. the motor is on the back on the printer and not right on top of the print head.

I personally wouldn't consider Nylon as one of the really flexible material, but that's my opinion. Never had kinking in the Bowden tube with Nylon either in my UM3E.