I rememeber something about a problem with these constant, they should have been corrected in one of the subsequent Addenda. If possible, procure 2007 edition and compare the constants.
Regarding the methodology itself, I concur with TGS4; moreover, if you would like to accurately check flange...
We are based in Europe and often our suppliers offer EN material.
The requirements of the API are pretty clear: Vendor shall certify that the material produced and tested according to a national standard meets all the requirements of API 650 Table 4-2. If it is not possible, Vendor shall choose...
If you are sure that you don't have anything on the bolted connection except pressure, then you are right (for a flange, for example, you may have local loads, flange deformation due to thermal effects or gasket relaxation, etc.).
The secondary stresses, as far as I know, are due (mainly...) to...