It may be worthwhile remembering that the 'Kellogg' method for including external loads in a flange design is reproduced in two forms in ASME III, the nuclear piping code so it does have some street cred. So far as the average flanged joint is concerned, there are so many unknowns such as actual residual gasket and bolt load, gasket spring rate and potential pipe misalignment that there is little point getting too technical.

If you want a truly new approach, and one which requires a huge amount of input data, look at EN1591, same as EN13445 App.G. It considers the whole unit as a bunch of springs and pre-defined shapes, then does a mini finite element analysis of the complete joint, employing a multiple step convergance solution. It also considers external loads.