The article cites a retardant advocate as saying "Deaths caused by furniture fires dropped from 1,400 in 1980 to 600 in 2004; a 57 percent reduction."
We know that almost all of these couch fires are caused by people falling asleep while smoking cigarettes.
According to the CDC, in the same period, cigarette consumption in the US adult population has fallen from 33.2% in 1980 to 20.9% in 2004. (http://www.infoplease.com/ipa/A0762370.html)
So a certain portion of the decline is due to the reduction in cigarette use.
Also, 43 out of 50 states now mandate "fire safe" cigarettes which contain substances such as ethylene vinyl acetate which increase the chance an unsmoked but lit cigarette will stop burning. The presence of these cigarettes has also certainly led to fewer couch fires.
http://en.wikipedia.org/wiki/Fire_safe_cigarette
It is unlikely that the entire 57 percent reduction in couch fires over 24 years is entirely due to the use of carcinogenic flame retardants.