I make countersinks as needed out of drill rod. Crude ugly things, nothing fancy. They have a pilot that fits the pre-drilled hole, this helps a bunch. I apply flutes by eye using a Dremil tool. I normally do two or three flutes. It does not seem to matter. I harden them then draw to a straw color. I then touch up the edge by dremil or cheapo diamond needle files. I then run them slow with oil.
If you run a drill bit or counter sink that has no pilot, in a preexisting hole, it probably will chatter, especially of you spin it too fast.