@JonBeardsley I don't think the approximation you propose is possible in general. For example, the inclusion of Spec F_p into Spec Z is not flat, but the obvious sequence using Z/p^n is not made of flat maps. I think it is more common to factor through something nice, like the inclusion into Spec Z_p (or Spf Z_p if you like formal schemes), followed by the flat map to Spec Z.