Oil and gas companies prohibit lots of things, some for good reasons related to the LONG design life of their projects, and others for not-so-good reasons. But that's not the question you asked: you asked whether there were CODE rules preventing their application, and in B31.3 there are not.
Flex hoses, properly implemented, can be real problem solvers and can make piping systems safer. Compare the implementation risk of these against expansion joints of various kinds...But hoses too are often mis-applied, in particular when they are used improperly to replace an axial expansion joint. A hose where the overbraid has been slackened by axial compression is little more than an under-designed expansion joint.
Service life depends greatly on service conditions. Hoses contain thin parts which are highly worked, which makes them vulnerable to corrosion and corrosion-related embrittlement in particular. The nature, direction, magnitude and frequency of flexing is also important.