What is the bike?
Yes, that looks pretty screwed up but there is really no way for it to "slip" because the little drive dog engages the chainwheel positively. Is the chain tight? I think you should fix it, even though it can't be the slipping.
If you are looking for exact factory matching stuff, it will probably have to come from the same kind of bike or at least similar. I am assuming that is a 24tpi crank. If so, a whole brand new BMX bottom bracket set would probably fit, as long as you used the whole deal. Individual parts probably wouldn't. To replace individual parts, it will need to be somewhat vintage.
In the old American standards from that period, 24tpi vs 28tpi made a big difference. Assuming 24tpi, the cups in the frame took a retainer that held 10 bearings. All the cups should interchange as long as the outside diameter is the same, and most are. Huffy used cups like through at least 1980, and probably a lot later. So did nearly all other American bikes with one piece cranks of that era as long as they weren't 28tpi Schwinns. From the prewar era, even Schwinn cups would probably fit. If the OD is wrong, you will have to find some cups for your particular make and model.
The bearing retainers, assuming 10 balls, interchange with non-Schwinn one piece crank bearings up to 1980 and beyond, and also prewar Schwinn. They don't seem to be that common now as new parts, but up through the 80s, it was the most common bearing. If your old retainers aren't shot, just pop new balls in.
The cones, assuming 24tpi, interchange with all 24tpi American ones up to the 80s or so. There are different styles on the outside with different looks, some use a separate dust shield under the nut, some do not, etc.
If it is a 28tpi crank, the cones have to come from a prewar Schwinn to fit without changing anything else. Postwar Schwinn cones are for a smaller 9 bearing retainer and a different cup, so do not fit quite right by themselves. The OD of the cups is the same as a standard non-Schwinn though so the whole postwar Schwinn setup usually fits as long as you change everything.
Slipping must be in the rear hub. I would tear it down and clean it out. Maybe you can see damage, but it's probably just all gummed up.