Have a mini-lathe, am making a gadget to pun on the toolpost so I can use
the lathe chuck as an indexing head and mill sections/slots whatever.

All my mills have a 3/8" shank with a flat.

Is a 3/8 hole bored in the spindle and a set-screw good enough?

Or should I make some sort of collet and holder?

If I make a collet, what keeps the mill from slipping - just friction, or is
there supposed to be some sort of method involving that flat?

Bear in mind there's not a lot of room...