I don't know the chemistry but it would be great to have cheap home tests for this stuff. The only available accurate cheap tests are for lead, for more comprehensive heavy metal tests you're looking at $200-400 and weeks of waiting.
AAC setups appear to range from $5,000 to $25,000 (depending on features like multi-sample processing automation etc.) at present. A lab capable of safely handling nitric acid digestion (fumes a bit) needs an effective chemical fume hood, which are at least $20,000 for a fairly basic small hood, and each metal you want to test for requires a separete protocol. See for example:
https://www.epa.gov/sites/default/files/2015-12/documents/70...
You can do a bunch of different metals at once with ICP-MS but those systems cost around 10X as much as AAC.