That looks like either an HK 91 type, or a SIG AMT barrel. Yes that is fluting, not rifling, both are roller-delayed blowback operating rifles, and require that some of the expanding gasses get blown back into the chamber to "float" the cartridge case so it will smoothly extract from the chamber.
Work-tank ofthe machine doesn't need to be as deep as the barrel, the ram-to-table max distance is what is crucial here. Just setup loc-lines supplying dielectric to where it is burning.
HK probably has highly specialized tooling for doing this that would be prohibitively expensive to replicate for small run, then there is also the problem of finding someone with an EDM with a big enough Z-envelope to burn these, there is a reason none of the contractors will touch this project.
The only way I see to burn these is to do a couple of flutes at a time.
Barrel locked into rotary indexer, set for six divisions, barrel canted at a 5 degree angle or so (and your electrode canted with the inner profile at 5 degrees also) 2 flutes per electrode, copper or copper-tungsten electrodes, depending on your power supply. Burn, and Turn
Depending on surface finish/power supply, each burn (2 flutes) will probably take only a couple minutes, even on an older machine. Once electrodes are cut and you have the machine set up for the job, you could probably get away with 20 minutes per barrel, start to finish.
'Slinger out.