LT3081 Precision Current Limit Programming
An 8 bit pot gives you 2^8 possible taps (256) so at best you could manage slightly under 4mV steps.

A 10 bit pot has 2^10 steps (1024) so in theory could give you your 1mA resolution in a suitable circuit. 

You are going to need a digipot that can handle 12V on the element, not a given as most of them are limited to within the logic supply voltage.

Were it me, I would be thinking in terms of setting a fixed current limit with this mechanism, then doing the current limit by using the Imon pin and an opamp or such to pull the set pin down on overcurrent, this has the advantage that such things as foldback limiting become possible, and both your control signals are now ground referenced and can be trivially generated.