The company is still in business and has a rather interesting, but odd to use, timeline on its website: http://www.brown-forman.com/company/heritage/
As I read it, the Brown-Foreman name would be post-1902. I don't see the King brand on their website, but they do have a contact e-mail: Brown-Foreman@b-f.com that you might use to inquire. I think the piece itself was a "hanger" fastened around the neck of a bottle of their product - they no doubt placed these in hopes that people would use them as a keychain tag or otherwise use them and be reminded to buy more.
John in ID