Why?
In the complex and expensive process of targets, effects, priorities and resources, why would you want to deploy FJ against helos? Where in any theatre does this threat exist? An errant helo ignoring all the rules/IFF/etc is more likely to be a crazy journo than a true threat. Kim is right about ROE and I sure there are others who remember the hassle of ROE and engagement criteria for FJ against Iraqi helicopters breaking the old BOLTON/WARDEN no-fly zones to commit mayhem on their own countrymen.
Any FJ on station is loaded for its primary and secondary tasks, so it's unlikely to get authority to expend ordnance until it is returning, even if it wanted to.
I know of one man who was highly successful in FW v Wessex 5 engagements, once he had been briefed on the route and was vectored onto them. He had a cracking eye for terrain and knew the ridges and pinch points that the helos had to cross. Then he flew head to head with flaps down and used his cannon.
The aircraft? A Sea Fury.