Flexi disc, sometimes known as a Sonosheet, is a kind of thin vinyl record. They were (and sometimes still are) often found in magazines or promotional print materials.
Example of a flexi disc in MB: http://musicbrainz.org/release/08a1beea-55f6-4c02-b0c6-f0fb92223d96

Further reading: https://en.wikipedia.org/wiki/Flexi_disc