I love the look of oil finished calls. And you cannot beat the durability. To me, those RNT's look 1000% better when they're oiled as opposed to that dipped finish. Especially the aged hedge! First time I've seen that on and RNT and I'm on board for sure. Darn nice work guys.
Boiled linseed oil is a pretty workable finish and has been used for decades on calls. No doubt it'll work fine. I don't use it because I don't think it offers the protection that some other oils do, but it will absolutely work. I'd re-apply periodically.
My preference is a product called Velvit Oil (not spelled Velvet) but their retail availability is pretty minimal. I have mine shipped in. A product that you can get at any hardware or paint store is teak oil. Teak oil has a thinner viscosity and more carriers, so I think you'll get better penetration with it. Tung oil works well too, but takes a long time to dry in comparison.
Whichever oil you use, let that call soak for hours. Totally submerge it, put a lid on it and forget about it for at least several hours. Some custom callmakers even pull a vacuum on their calls that are submerged in oil just to get really good penetration. That isn't necessary, but a good long soak cannot hurt. As soon as you remove them, wipe them dry and then check them periodically for days and re-wipe as necessary. The wood will often sweat out extra oil, which usually wipes right off unless you leave it for days....At which point it might require a little light work to get it off.
The only think I'd caution folks against is using vegetable oil or any other sort of cooking oil. They'll go rancid in the wood and can make you sick.