The main threat from the media particles in the flash hole is that if your sizing die is used afterward and has it's decapping pin in place, the media particle can steer the pin to the side where it hits brass and breaks off. If you miss getting a particle out and are not running another decapping pin through after the second tumble, the primer can push the particle out of the flash hole for the same reason it can push powder out of a flash hole. It doesn't wait for plugging powder grains to finish burning; the primer is done much faster. For match grade rifle loads it would be best to knock the media out of flash holes because it can, as it is blown loose, alter the spark spray pattern and that may affect muzzle velocity variation a little. It's mainly a long range consideration.
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