I don't know of any specific load, but for starters: With a 169-grain gas-check in an '06, 20 grains of 2400 gives around 1,900 ft/sec or so.
So, somewhere around ten grains of 2400 or equivalent burn-rate powder oughta get you in the ball-park.
We got into this subject, here, several months back. "Reduced loads for ?", I don't exactly remember. I don't remember if oatmeal as a filler was panned or not.
I used to use five grains of shotgun powder with a 00 ball in the '06; no filler. I got reasonable squirrel-range accuracy.