My parents had one of these , but it was a dark green or blue color. The city outlawed burning and by some time in the 70s, that was the end of burning our trash. I didn't miss the emptying of the ashes!
I grew up in Eagle Rock, a little neighborhood in the North of Los Angeles nestled between Glendale and Pasadena. The area was largely developed in the twenties and thirties and many of the houses in the neighborhood had brick contraptions in the backyards that looked like some sort of oven or BBQ with tall brick chimneys. In reality they were all built for burning trash, though none had been used for decades. They were similar to this design. I’ve never seen one like the one you posted above. Didn’t even know they existed.
We were one of the few families on our street/block that had an incinerator. It was so convenient...but oh, the pollution, I'm sure not tooooooo goooooood.
Interesting design there - looks like a back yard cooker.