1
general::
Also, chew the rag. Chat in a friendly, leisurely way, as in Let's get together for coffee and chew the fat, or John and Dave spend hours just chewing the rag. Before the 1880s in Britain, chew the fat meant "to grumble or complain," and chew the rag Also has been used in this way. Today both expressions are largely synonyms for a friendly talk or gossip session. Why this idiom uses fat and rag is not known, but some speculate that fat refers to juicy items of gossip and rag to ladies' sewing circles and the cloth they worked on while chatting.
American Heritage Idioms
2
general::
Phrase(s): chew the fat [and] chew the rag
Fig. to chat or gossip. • Sit yourself down and let’s chew the fat for a while. • We were just chewing the rag. Nothing important.
McGrawhill's American Idioms And Phrasal Verbs