They certainly had them, at least as far back as the 1970s, and perhaps even into the 1960s, though allotments to various squadrons and aircraft could probably be hit or miss.
Surprisingly, even the FAA of the Royal Navy had to make do with their Sea Harriers in 1982, when they went to war against the Argentinians. They stuffed their airbrakes with chaff, as mentioned above, for a one-time, desperation use measure.
Not sure if they had flares back then, or got them on their way to/after being in theater for a bit.
I find that to be truly astounding during the early 1980s, at what was really pretty much the height of the Cold War tensions as well, for a major NATO ally, and "1st Rate" military power.
I'm inclined to believe that the Mig-23s would be more likely to have both than the older Mig-21s, generally, but really all should have them, since the measures are so cheap relative to the value of the jets and their pilots. That's especially true when one considers how well these seem to work against older, and mid-Cold War missile tech.