I only get 9 "hits for vibration in the 2002 NEC, none of which seem to apply.
368.28 (Bussways over 600 volts)
545.13 (Manufactured Buildings)
550.16 (Mobile Homes)
552.48 (Park Trailers)
695.12 (Fire Pumps)
I looked in 450 and some raceway articles and could find no requirement to flex in transformers, I have done it with many different methods, pipe, trough, flex, etc.
What I found strange is no requirement to use a flexible method to a motor.
Construction & Maintenance Electrician