Refer the MTD guideline. This will give you qualitative but not quantitative solutions.Actually if the LOF is greater than 1, bending stresses have to be computed ( the otjer corrective actions are increase in all thickness, increase in diameter etc, more supports etc )as suggested by me in my previous post.However I will not be able to reproduce these equations.

However flow induced vibration is a low frequency vibration as opposed to acoustic vibration which is high frequency and in flow induced vibration, it is basically planar wave propagation and hence confined to smaller diameter pipes ( typically) less than 10 inch. Hence I don't see possibility of flow induced vibration in large flare systems but there is every possibility of acoustic vibration( high frequency acoustic vibration is not that dependent on rhov^2 but is dependent on Mach no times pressure drop)

Regards