You cannot use appendix V to adjust the allowable stress for the design condition that is used to establish wall thickness. It is used to evaluate short term variations that are permitted by para. 302.2.4.
Don't forget the new "W" factor for elevated temperature welds.
With respect to flexibility and displacement stress limits, the rules in B31.3 are designed to consider creep fatigue; it is not necessary nor appropriate to us Subsection NH of Section III.
The B31.3 rules do not directly consider fatigue or creep fatigue due to pressure cycling, so you will need to establish your own assessment method for that. If you choose to use NH, and I am not advising you to, you should fully understand the rules. In almost every supposed NH assessment I have seen, some small bits and pieces of the rules were used. A good description of the rules is provided by Bob Jetter in the "Companion Guide to the ASME Boiler and Pressure Vessel Code," 2nd edition, Volume 1, ASME.
_________________________
Chuck Becht