Using two tires on one wheel to prevent punctures? I have 20 x 3.0"tires, which seem to be pretty hard to find--especially with nice puncture-resistance like Schwalbe's "Smart Guard," or something of that nature.  Unfortunately, I'm definitely getting more flats.
My mechanic told me that I could double up on the tires--put old tires underneath the new ones so that it forms essentially an inner tire liner.  He did this in the good old days, apparently.  He in fact recommended that over other commercial products (Tire Liners) because apparently Tire Liners cause flats in themselves.
I have an e-bike, so I wouldn't mind the extra weight and might give it a try, but was wondering if anyone still does this today and if there's anything I should be wary of when / if I try it out?
I'd just buy tyre liners (example from Zefal).  They're made from tough polyurethane which many sharp things won't get through or at least not quickly. I've used cheap (unbranded eBay) ones on a cheap bike when I didn't want to buy expensive new tyres, and they worked well, with one issue, probably what your mechanic was thinking of that was easily solved by taping over the end.  They can be cut down to fit your small wheel, and it looks like the ones I've linked are made wide enough. Another popular brand is Mr Tuffy, though I've never used them.

If you want to try recycling instead of buying, then use the tyre liners as inspiration.  Here's Zefal's video on fitting them, so you can see the approximate proportions.