There are a couple of things to do, I'm going to assume you have the chuck close but not tight enough to make the mill "stay" in place.
I use paper towels, I place the towel over the tenon then slip on the mill. I've used as much as three layers of towels. I tried toilet paper, tissues, paper towels like Bounty, but the ones I found that work best are the brown paper towels that come out of a wall mounted dispensers. You can buy them at a janitorial supply. Find what works best for you
I've seen, but not tried, people using chalk on the tenon.
Also, the tenon needs to be "square", if it's tapered, you'll never get it to work right.
Lastly, the tenon needs to be long enough, you'll need to experiment with the proper length.