Below are the instructions which came with the Eddie Dow fork conversion way back when. He says 1/3 pint (about 190ml) of SAE20 which is a bit less than the original BSA 213ml.
Have had a few of these dampers conversions and found that there can be some variation of length of rod supplied by different makers. The dampers do need to be in the oil or you will hear an audible slap as the damper meets oil and the intended damping effect will be compromised.
For best effect you may need to experiment with oil grade and amount.