This is the band's first show ever as "Tony Flow and the Miraculously Majestic Masters of Mayhem". It was a one-time opening act. The date listed on the official website is February 13th but the timeline on "An Oral Visual History" book says February 6th.
Both of those dates were on a Sunday and the "Rhythm Lounge" only opened on Thursdays, just like Blackie Dammet briefly mentions on his book about this show: "that memorable Thursday night in February 1983 when the dynamics of music changed dramatically and altered the balance of the L.A. scene", which makes us pretty sure that neither of those dates are correct.
So far the real date still remains unconfirmed, but our guess is the show took place on the 17th.