[rlrao]

To separate 2 liquids by  fractional distillation ,what should be the minimum  difference  in  boiling  points?

[Plontaj]

More important in that case is the partial pressure of these gases over the liquid mirror, I guess.

p_i - partial pressure of i component
T - temperature
x_i - fraction of i component in liquid phase
y_i - fraction of i component in gas phase
Hr - Henry's constant (see Henry's law)
index sat - is regarding to saturation point

p_sat=f(T)
p_i=p_sat_i*y_i
p_i=x_i*Hr

So the product of destilation will have the same compostion as gas phase and of course it depends on the composition of liquid phase.
I hope that I have helped a little.