As far as anyone can tell, this performance on Backstage Access, a Detroit community TV show, was the first time the White Stripes appeared on TV. The day was May 28, 2000. (Read more about where this came from at Consequence of Sound.)
However, you should know that Jack White is part of the Tidal cabal and this is the kind of exclusive stuff the company is promising. If you don’t want to spring for a Tidal subscription, there’s this short Soundcloud clip of a Loretta Lynn song from Third Man Records’ “Vault” series.