The SA-11 missile (NATO designation GADFLY) is an active radar homing device, so chaff dispensers could have been at least somewhat effective against it. The problem is that any kind of missile countermeasures require a detection system and a maneuverable aircraft, neither of which civilian airliners have*. You need to be warned of the incoming missile, be able to project its course, and maneuver away from it as you pump chaff into its path to mask your escape. Not an easy or practical matter for a loaded airliner.
*It is belived that El Al, Israel's national airline, has onboard countermeasures that help defend against missile attack. These are typically installed on US combat aircraft and front-line cargo carriers. They are believed to include chaff and flares to divert radar and heat-seeking missiles, and even lasers to blind incoming heat seekers. Unofficial sources say these same type devices are found on Air Force One.