Proper way to oil a neglected flute and fife

[Rapparee71]

I pulled out my Casey Burns standard folk flute today to oil it. I had not oiled it in a while. I know, BAD! I have been dealing with a lot of health issues over the past couple of years, and moving across the country, etc. I was wondering if there is a correct way to oil the head joint? I just put some oil on a piece of silk, and gently pushed it in and wallowed it around, hoping to coat the bore. I ran the silk through the other two joints, the same way. I also coated the outside nicely and am letting it all soak in for a bit before I have another go at it.

I actually heard back from Mr. Casey Burns and he said that the "rough" places are nothing to worry about. He actually does not polish the bores of his flutes to a high degree and it actually helps the sound in some cases (I am paraphrasing).

There is also my fife that is one piece. How does one properly oil them?

Thanks!

P.S. I am actually thinking of going to one of Casey Burns' small-handed ergonomic models. I have always had a hard time reaching some of the holes, especially with the ring finger of my left hand.