What is your specific application?
Flame straightening is not endorsed nor prohibited by ASME Boiler and Pressure Vessel Code. This is a process, and as such, must be controlled by a detailed process procedure that is reviewed and accepted by the Authorized Inspector.
If you intend to use general heat and force to reshape or move an object, yes, I have seen it performed under controlled conditions with a procedure and only used on carbon steel. If you intend to simply re-round an object using only spot heating (aka flame straightening), this will not work.
Typically, the application of flame straightening for structural beams or shafts requires very localized or spot heating (torch heating). Because of spot heating affects, flame straightening will in most cases exceed the lower critical transformation temperature especially for low alloy steels. There can be no stress relief or reheat treatment of the object after spot heating because it will undo the residual stresses applied during spot heating.
I would not permit the use of "flame straightening" to re-shape a pressure containing object. The application of general heat and mechanical force can be used, provided the temperature used during general heating is kept 50 deg F below the published lower critical transformation temperature. For 2.25% Cr-1%Mo (P22) low alloy steel the published lower critical transformation temperature is 1480 deg F.