As far as I know anyone can hang out a shingle and perform fire assays. Unlike labs producing certified results for waste treatment and similar analysis, where the states have Environmental Laboratory Approval Plans (ELAP). Fire assayers only have a work history to tout on their shingle. quite a few have come out of big name labs like LeDoux or Walker & White but there is no criterion.
The entire premise of fire assay for settlement involves two assayers getting an identical sample and the results are compared. Any differences, over the splitting limits specified by the refiner who took the samples, are settled by an umpire lab. All refiners have a list of labs that they accept results from for umpire analysis. Whom ever's result is closest to the umpire result wins the decision. A good test of an assay labs quality is how many times have they been to umpire, and how many times have they won. I would think that to operate a successful assay business a lab would also need either an Atomic Absorption Spec or an ICP for determining PGM's. Gravimetric PGM's take too long to be done profitably. That is in addition to the full compliment of fire assay equipment.
Of course a degree in chemistry would also help and should be noted on the shingle too.