What are these accelerating flare countermeasures called?
These are generally called "propelled flares", or sometimes "aerodynamic propelled flares". Some antiaircraft systems are able to distinguish between a normal flare and the aircraft, as the flare is not travelling along the expected path of the aircraft. Aerodynamic flares were first developed to allow the flare to continue along the path, but as antiaircraft systems developed further, they added a method of propulsion (which uses the same fuel source as the flare itself), to ensure that the flare continued alongside the aircraft, slightly angled away, at a similar speed. This does a better job of confusing these aircraft systems, but it's a fairly "niche" type of flare that is meant to combat conical scanning.

I believe the ARM-031, MJU-47/B, and MJU-71/B are all forms of propelled flares.