Much like sucking a dick, however this phrase is much more aggressive. Chugging a dick involves "bouncing" the cock in your throat for a longer amount of time.
"Oh snap, that girl must be chugging a dick, she doesn't have a gag reflex."
The act of engaging in oral sex between two or more bros. Additionally, this phrase can be used to denote any form of sexual contact between said bros.
"Hey CJ, I had a great time chugging a bronson with you last night!" said Steve.
"Yeah!!! That was super!" replied CJ.