The provisions of 6.13.6.1.3b only apply to "Flange splice plates and their connections", not to the flange itself. So, the short answer is that you don't have to check the flange according to the provisions for splices.
The "new" method introduced in a previous version as another option, but now the only option, is a simplified, even more conservative approach to splice design. For the splice only, it essentially ignores the moment capacity of the web splice, so that the flange splices carry all the moment. The web splice carries only shear. Moment due to eccentricity of shear on the web splice is ignored completely.
With a splice at a girder section that is near capacity, it would be prudent to check the flange for yielding on the effective section and fracture on the net section (using Fy and Fu, respectively), but it is reasonable to use the elastic section properties of the girder and the factored applied forces, rather than the design forces for the splice. This is reasonable because the girder is a single cross-section right up to the point of the splice. The flange splice plates are not part of a larger section, so they must carry the accumulated force across the splice independently.
