You write the spec. It can be cosmetic or physical, or both. "No flash" is an enigmatic term sorely lacking in hair-splitting detail. The one time I've had to specify, we just called out max profile dimensions of the parting line area, including a "no hand trim" instruction.
There are tools which simulate the 'does it cut your finger test'.
They have some kind of roll of tape and you roll it along the surface, if it cuts the tape it fails or something like that. So you could specify a requirement to pass that kind of test, I suppose.
It's come up before in relation to 'remove all burrs & sharp edges' as often specified on machining drawings.
Arguably you really should give a definite limit, but it's one of those things that it seems a lot of effort for something that you usually get any way etc.