I did a little research on the place, and it opened in October 1977. Previously at that 4226 University Avenue address was the "Palace Card Room".

The 1978 and 1979 San Diego White Pages, list James H. Fisher as the owner, and the 1980 White Pages list John R. Romero as the owner. I don't have access right now to later White Pages.

The card room was open until at least 1984, but by 1993 the "My Place Card Room" is at that address, and is listed as having 4 card tables.

Below is the 1980 San Diego Yellow Pages listings of cards room. The Flamingo Card Room is listed 3rd from top on the first image. As you can see, San Diego had a lot of licensed card rooms. Many only lasted a couple of years.

I have created a document that has most of the San Diego Yellow Page listings for "Card Rooms" from the 1950s to 1980. If anyone is doing research on San Diego card rooms, and think they would find it useful, email me. I can send it to you as an attachment.