When were flares first used as IR countermeasures, and by whom?
The document Genesis of Infrared Decoy Flares- The early years from 1950 into the 1970s by Naval Surface Warfare Center has a lot of details about the work done on decoy flares in the initial stages, at least in the US.

According to the report, the first use of IR flares was not as a decoy, but as a tracking device for drones. The T-131 flare was used in this capacity. From the report:


  NOTS, China Lake was involved with infrared target augmentation since 1954. ... The T-131 tracking flare developed at NOTS was the first infrared source for drone use. Six to sixteen of these are needed on the F6F-5K drone to provide a suitable signature.


The first IR flare developed as a countermeasure is the NOTS Model 704, which was developed around 1959. However, the studies on decoys for IR started in the mid fifties, though the concept of using flares came later (the initial concepts were towed decoys). From the report:


  The Hayes Corporation, Birmingham, Alabama initiated infrared countermeasures and radiation suppression studies in 1955. ... There was a need about 1957 to create a decoy device that would simulate the signature of a turbojet engine. Instead of the pyrotechnic decoy flare approach,
  ... proposed an inflatable envelope that absorbs the energy from a self-contained pyrotechnic and re-radiates this energy at a lower temperature approximating that of the heated surfaces of the turbojet engine.


Initial flares (RR-77, probably) were fitted in the B-47 and B-52 bombers, which were deployed through the AN/ALE-14 dispenser around 1960. Though the report has indications that the flares were used in the Vietnam war, there is no data on the exact time and location of the use of flares in combat. However, we can be sure that the IR flares were used in combat in Vietnam. The report says,


  In 1967, Dr. Edwards of Air Development Test Center at Eglin Air Force Base, requested Picatinny Arsenal to improve the ALA-17 flare. The Air Force wanted a quick fix to the poor rise time of the ALA-17 flare. They also required that a single ALA-17 flare would have decoy capability to protect B-52 bombers in Southeast Asia against seekers operating in the 2μm to 3μm and 3μm to 5μm bandpass.


indicating feedback from combat operations. Though I'm sure that the Soviets too were developing IR flares at the same time, not much detail is available about their effort.