A well-placed flyer can reach the eyes of thousands of people per day, regardless of which social media platform they use, if any.
If you make a flyer for an event, share the file online and encourage others to print them out too.
Before sharing, remove the metadata with Scrambled Exif on Android or Metadata Anonymisation Toolkit on Linux. Sending a copy to a friend? Send it over Signal.
The paint can mimeograph is really cool but it looks like the special waxed stencil paper is basically out of production (aside from a Japanese artist who makes it and is willing to sell it internationally). Do you know of another source? It sounds like it can be made diy but that is an extra step in making the flyers.
(I was thinking about how one might combine that old tech with a modern laser etching machine for some especially fancy stencil work.)
The second link for the even simpler hectograph gives some suggestions. Are you USA based?
If so, I found this supplier using the search term “mimeograph masters “.
https://www.officedepot.com/a/products/852830/SKILCRAFT-Mimeograph-Paper-Letter-Size-Paper/
That’s for 10 reams and it’s discontinued but it was the first clue for a US domestic supplier that isn’t exorbitant etsy prices, which seems a bit much, but I will keep digging to see if I can find a better source.
This link from the same site has a long discussion of the paper needed for the masters.
https://www.mimeographrevival.com/posts/stencil-paper/
It looks like paper that just has certain properties to hold onto the ink well enough without bleeding so it can then be used to make multiple impressions.
The hectograph method my mom used back in the day involved hand writing on the master sheet as it lay upon the prepared ink bed, then using the inked back side of the master to make enough copies of a worksheet for her classroom. So some experiments may be in order.