There was a Plastic-Man centered annual a few years back which dealt with the introduction of Plastic Man to Woozie Winks. During that adventure, Plas is shot with a number of darts that cause him to "bleed", and Winks notes that his blood "smells just like airplane glue". (Winks, who was previously a talented spy and assassin, is made permanently "woozy" by his exposure to this blood while in an unventilated space.)
I have no idea if this story is considered canon or not, and we've certainly seen Plas get injured in a number of other instances and not bleed glue, but if you're willing to accept for the moment that he does have some sort of chemically volatile bodily fluids flowing around in him, it's not out of the question that his digestive process involves some kind of super-potent solvent that immediately dissolves anything taken into his body and distributes it throughout his form in moments (he doesn't seem to have a functioning heart, either, so it's safe to say that he could move fluids around his body at will, given his powerset). That would eliminate gaseous byproducts, or distribute them out far enough that they could be released in tiny amounts through pores rather than in big...er...eruptions.