Just to clarify the title: not sure if this dialect always switches the "p" out with the "ʙ̥". For example, if the p is in the beginning of word, maybe this doesn't happen.
Also, I'm not sure this dialect even exists. I have definitely heard this kind of pronunciation, like with the word appreciation being pronounced with a voiceless bilabial trill instead of the voiceless bilabial plosive that standard English uses. However, this may be an ideolectic or even situational (to add more drama perhaps) pronunciation.
So my question is this: does there exist an English dialect/accent that does this?