I'm not a welder (machinist by trade) but I do know if you weld it it'll probably pull/warp the flange, everything warps when you weld it, it all depends how much heat you throw in it. If you know someone who TIG welds, that would cause the least warping and you might not have to remachine the flange. If it does warp, it is no big deal to chuck it in a lathe and take a skim cut of the face to make it flat again. What kind of diff is this axle out of?

You could PM DrDiff on this board and ask his opinion, he's the resident expert on all things differential

Just reread your post, is this the rear axle or the front hub?