History of stuff - how do they do the shimmering stroke affect?

Didn't have time to watch it all, but...
The 'Shimmering' seems to be on the still aspects of the animation, for example, the guy shining the shoes about a minute or so in, his body is still and shimmering but his arms are moving and don't appear to have the effect on.
It can be done by cycling between two slightly different frames. You'll probably need to make each element of each character in Photoshop and decide what needs to shimmer, then make a slightly different 'dupe' layer. Build each character in it's own comp in AE and you might want to build the shimmering components in their own comp so you can just make a 2 frame shimmer, nest that in a build comp and repeat it to fit. It might need more than 2 frames to see it working so have a play to see what looks right.
Hope this makes sense, i think it should work!
It reminds me of a cartoon series from the 70's, Roobarb & Custard, all hand drawn and coloured with big marker pens for speed

You are looking at Flash animation and it is quite easy to attain the effect you are looking for.
You essentially have two options:

1) Draw a keyframe (make sure your lineart is made of fills either by using the brush tool or converting lines to fills).
Turn on onion skinning so you can see the previous keyframe
Make a new keyframe and trace over the onion skinned image. (your art will be a bit different than the earlier drawing)
Loop these frames.

2) Draw a keyframe as before.
Duplicate the keyframe.
Use smoothing on the lineart 1 or more times until the lines look different enough to please you.
Loop these frames.