Detectable elements using flame AES
but I can't find anything because flame AES seems to be quite outdated.

Please don't say that you cannot find anything, this is the reason (i) why physical libraries still exist and (ii) right key words are needed for proper literature search and (iii) not everything is available on the web free of cost.
Most of the metals are detectable by flame atomic emission spectroscopy. All you need is the right flame. The instrument, called the atomic absorption spectrophotometer, works perfectly in atomic emission mode. There is no separate instrument for Flame-AES.
The flames are quite &quot;cold&quot; for non-metals like sulfur, carbon, nitrogen, and noble gases. ICP also works poorly for non-metals.