A tale of two chains... the Western flyer (original) skiptooth chain was pretty crusty. I'm using the one from the 1942 girls "donor bike" as the main component but will need to borrow a few more links from the original to make up a slightly longer chain. The '42 has a master link already, which helps.
For the uninitiated, "skiptooth" chain has short and long lengths unlike modern chain and they are expensive to replace. I'm going to use what I found because I like the aesthetic of making do with what you find and keeping as original as you can in many ways just so nothing gets wasted.
You can see here that I was able to work the '42 into a fully flexible chain by the recommended method - cooking outdoors on a hot plate in some heavy gear oil at a low temp - less than 200 degrees - for a few hours so the metal expands and the oil can get into every where.
The real trick is going to be if this same method works on the super-crusty original chain well enough to rehabilitate a short section. As shown below, the original chain barely flexes at all. This is as much as I can move it as found.
What you see here is the difference between a bike that was in a garage and a bike that was out in the elements of Texas for years. The garaged bike chain is almost new in comparison, even thought the paint job on the frame of the bike kept under a roof is seemingly more similar to the one left outside. Different components break down at different rates. Chains don't like to be mistreated!
Here is a close up. As you can see the '42 is far from perfect but it's able to flex again with about 15-20 minutes of manipulation by hand to break free all the sticky spots. The crusty one will be a different story. After I flexed it around a bit it got another bath in hot oil for good measure, and as thorough a cleaning as I could give it with a wire brush.
The original chain will get the cup brush power drill treatment and an overnight hot oil bath. Again, not too hot so the oil doesn't burn off or the metal take too much stress. You just want to get the oil everywhere it can go. I'll probably brush naval jelly on the crusty one as well. The goal is only to salvage a few inches of the best links to add to the '42 chain as needed for length.
We shall see if the adage is true that a chain is only as strong as its weakest link. I'm sure if this chain ever fails it will be on the oldest section.