B31.3 will permit you to use any B16.5 flange durably marked as such with no subsequent testing required by you as purchaser. B31.3 (from 2010 on) requires you to have a number of mill test certificates for such components "...in a quantity sufficient to satisfy an examiner"- that means you don't need a MTR for every component, nor is item by item MTR traceability required. B31.3 also does not require that those markings be legible after fabrication of the piping system is complete- polishing, galvanizing, painting or other operations may remove the marks or make them illegible.
If your flange was 4500# instead of 2500#, now the special rules of Category K kick in, and MTRs are an absolute requirement.
The manufacturer must do certain testing and possibly heat treatment depending on the material used to make the flange. For carbon steel, we would normally require only a mill test certificate as evidence that such testing/HT was done. And yes, there is a possibility for fraud on the part of the manufacturer if they were to "utter" a falsified MTR.
In Canada, pressure retaining components used in pressure piping must also have a Canadian Registry number (CRN). Regrettably, separate CRNs are required in each province of Canada. The CRN requirement is, in our experience, widely ignored in many provinces in practice, but not in all.
Your client may require additional testing- they're paying the money, and it's their prerogative. But they cannot claim that such testing is a code requirement.
After attachment to the piping, you need to test the assembly by a hydro or pneumatic test, and you need to do all code-required NDE on the weld seam.