film techniques - First Hollywood movie with "flashbacks within flashbacks within flashbacks"?

As mentioned in the Wikipedia article on narrative uses of flashbacks:

An extremely convoluted story may contain flashbacks within flashbacks within flashbacks, as in Six Degrees of Separation (1993), Passage to Marseille (1944), and The Locket (1946). This technique is a hallmark of Kannada movie director Upendra whose futuristic flick Super (2010) is set in 2030 and contains multiple flashbacks ranging from 2010 to 2015 depicting a utopian India.

IMDB flaged also Enter the void (2009) with this technique. Seems that only these movies used this kind of brain teaser. As I found only these titles, i can answer your question saying that Passage to Marseille (1944) was the first movie using this technique. If you are interested you can give a look to the detailed plot here (SPOILER) looking how the flashbacks were actually mixed.