The original "Six Flags" was Six Flags Over Texas, an amusement park in Arlington, Texas (between Dallas and Fort Worth) opened in 1961. It was a reference to the six flags that had flown over (parts of) Texas; Spain, France, Mexico, the Republic of Texas, the US, and the Confederacy.

The company went on to open Six Flags amusement parks in various other places in the US, keeping the name whether the place ever had six flags or not.

Burbank is a suburb of Los Angeles. It has been the butt of many jokes. Johnny Carson (late night talk show host) often referred, humorously, to "beautiful downtown Burbank". There has never been a Six Flags Over Burbank. It's just another joke.