A quantum flux regulator was a type of 24th century engineering tool.
After spending twenty subjective years in an Argrathi prison, Miles O'Brien worked with Jake Sisko in retraining his engineering skills, so as to not embarrass himself in front of the repair crews, by reviewing various engineering tools in the cargo bay.
Among the tools he recognized were an interphasic coil spanner, an ODN recoupler, and with a bit more difficult, a quantum flux regulator, Mark III. (DS9: "Hard Time")
The use for this tool is unclear, however, by name alone, it would be suggested that it has the ability to regulate something that generates or exhibits a state of quantum flux.