As I've been having problems lately seating my primers to correct depth, I've taken to first decapping using a universal decapper. Then, I soak my brass in Dawn, Lemon Shine and a bit of dishwashing detergent and very hot water. Without tumbling, this formula burns dirt and tarnish off the shells, inside and out. Then they go in the vibratory tumbler. Unfortunately, Walnut media tends to clog in the primer pockets with the result that some get clean and many don't. As for media clogging the flashhole, I understand that primers are capable of generating 5000 PSI pressure on their own. No need to worry about a walnut kernal in the flashhole.
I think current state of the art is wet tumbling with SS media. Shells, inside and out, including the pockets, come out like absolutely new.