You got a few choises. 

Based on what can be seen on the pics it looks like a impact damage, not a fatigue break. The hub may hide some invisible cracks somewhere.

I don't think that area is subjected to a overly lot of tension or a ovely lot of varied strain, but because both sides of the flange are machined, there is no room to leave any weld material except precisely the thickness of the existing material.

Of course it can be welded, turned, machined or ground back to very close to original. That takes some expert welding to build up a new bit of flange with a flawless weld remaining. On top of that there is holes to be drilled right in the weld for the spokes. 

The bits could be brazed, but that isn't restoring the full strength. 

What will happen if a bit of the flange brakes off entirely?  The wheel looses stability, the rim becomes warped and a few loose spoke ends starts to flail about.

There is an excellent repro hub readily assembled with a new brake drum to be bought or you can try to find a used one.

I would explore those alternatives first. 

Isn't the new hub fitted with common Timken conical roller bearings?? It would be daft if not! Roller bearings is a such vast improvement both in stability, ease of service, adjustment and rate of wear over the loose ball bearings so it is a no brainer. If that is not the case I would modify them to take that or common ball bearings because the older loose ball bearing is nothing to strive to use (in fact I would contemplate send the hub back and complain!). If you got Timkens, the outer race is a part of a new bearing even if sold separately and I wouldn't bother use the old race even if they were looking good...

The older loose ball bearing outer race is a pain in the ass. I know they can sit like hell in the hub and are quite fragile as they are thin at the rear wall. But if you are lucky they might be extractable. That goes for the Timken race too. It is a matter of getting a gap at the rear where a collar extractor can grip the edge. Brute force might fracture the race so you got heat and cold to work with. Heat the hub and chill the race with some really cold stuff, like co2 dry ice. Maybe you have a company that work with air con, cryo tech, laboratory, or the like near you. Chill and bang the hub against wood or the like, then you might get lucky that they fall out or get a grip with an extractor to pull with. Good luck!

It is standard bearings, and they are sold separately in 2 pieces, inner race with rollers and the outer race. Timken #1729 and #1779. Should be available at any bearing shop. Recommended is to change both parts at the same time as they wear together. The old hub or place the race was mounted is distorting the race a bit and the rollers have worn a pattern in the race. Remounting the race could alter the surface and in time ruin the bearing. Now, the wheel is turning slow, the load is light and the play is a lot larger than say in a presicion high speed machinery so the danger is not imminent or severe assembling an old bearing, but a quick check on the net finds the cost of a new complete bearing is about $35.